I think you are right in saying 君がくれたもの doesn't have to be a physical object. It could be life experiences, an understanding of things, etc. The common thread seems to be that these are things that can be kept.
On the other hand, 君がくれたこと would, I think, often be understood as 'the fact that you gave to me' ('the fact of your giving to me'). 君が教えてくれたこと 'things you taught me' makes sense, but 君がくれたこと '(abstract) things you gave me' doesn't make so much sense.
Your question is difficult to answer because of your use of the expressions 'add value' and (particularly) 'imply the significance/worthlessness of'. These represent to me a misunderstanding of how こと and もの are used.
What makes discussing this difficult is the fact that substituting one for the other does not necessarily mean a simple change in nuance of the word 'thing', because もの and こと actually have other uses that are quite different from each other.
For instance, 勉強したことがある/ない means 'to have studied / not to have studied'. 勉強したものだ means something like 'used to study' and is a reflection on how much you used to study at some time in the past. What this means is that swapping one for the other in a particular context could result in completely different meanings, meanings quite unrelated to the opposition that you're trying to establish here.
But there are cases where there seems to be interchangeability between こと and もの. For instance, both 勉強したこと and 勉強したもの exist.
勉強したこと simply refers to content that you've covered in a lesson or course. For example, 勉強したことのまとめ means a summing up, or summary of what you've studied. There is no implication that what you've studied is trifling or insignificant. There is, perhaps, an implication of objectivity. It just means 'things that you've studied' -- no value judgement.
勉強したもの is similarly used for content that you have studied, and is generally very little different in meaning from 強したこと. If there is any difference, my feeling is that it suggests that what you studied has more content, more 'weight', or perhaps is something that remains with you (i.e., things you have 'learnt' rather than things you have 'studied'). But there does not seem to be a very clear difference between the two.
Take another example.
言っていいこと means 'something that it's ok to say'. The implication is that there are some things that it is ok to say to people, and there are some things it's not ok to say to people (言っていいこと、言って悪いこと). This is a social or perhaps moral judgement -- for example, don't say things that will hurt or offend people. こと here will tend to refer to the actual words that are spoken. For example, 「太ったね！」は言っていけないこと。'"You've put on weight!" is something you shouldn't say to people'.
言っていいもの is somewhat different. For instance, it could be used in expressions of describing (これは完全なフィクションと言っていいものだ. 'It is something that could be described as pure fiction'). When used to refer to saying things, unfortunately a different meaning can also come into play. The meaning of もの can be understood as 'Is this the done thing?' rather than 'Are these acceptable words to use'. One example from the Internet is 私は彼に「会わないで」って言っていいものなんでしょうか？ Here the word もの doesn't refer to the words 会わないで, it is asking for a judgement on the acceptability of a telling someone not to meet. That is, it is asking whether it is acceptable to make such a request, not whether such words are appropriate say to a person.
I realise that I haven't given you a good explanation of how to use こと and how to use もの, which makes this unsatisfactory as an answer. My understanding of the difference is that こと describes things in a more abstract manner, used of facts, actions, or words. もの is used of more substantial things, including physical objects, and abstract things that can be the subject of thought. The problem with most dictionary definitions is that they are too vague or abstract to enable you to distinguish the two.
However, what I can say is that your understanding here is incorrect. Using こと doesn't make something trifling or worthless. Using もの doesn't necessarily 'add value', although it may add weight.
I struggle to answer your question because you seem to be asking:
"By using もの instead of こと here, is it indicating that this something has more value?"
"Is that because もの refers to physical things that it implies more value?"
The problem here is that we have to narrow the context and syntactic environment right down, excluding any extraneous elements, to get the question to make sense. Specifically, the context is くれたもの / くれたこと (past tense verb + mono/koto). Swapping structures around can very subtly alter the meaning and frequency of expression. For example, ものをくれる (noun + verb) tips the balance almost completely in the direction of 'give a physical object'.
As for ことをくれる (noun + verb), this is used, but the sense is very vague. From the Internet:
たくさんのことをくれる 家族にも 両親にも 親戚にも お友達にも 今年の最後に 『ありがと。』
To our families, our parents, our relatives, our friends who give us so many things, for the last time (or the end of) this year (we want to say) 'thank you'.
嘘つきだろうと 落ちぶれだろうと やさしいことを くれる人ならば たとえ世界が空から落ちても あたしは あの人をかばう やさしくしてくれるなら
(From song lyrics) No matter if they are a liar or a drop-out, if a person gives me tender things (?), even if the world should fall from the sky, I will protect that person, if they are tender to me. (Notice that やさしいことを くれる is rephrased as やさしくしてくれる in the second instance. The meaning of やさしいことを くれる thus seems to be 'tenderness', or 'be tender to me'.)
ドラマで共演しているソン・イェジンに対して「多くのことをくれる女優」と評価した
Son Eijin who had a co-role is recognised as 'an actress who gave us a lot'
初めてのあのライブで、あの音で、完璧に心を打ち抜かれました。 それって、とても素晴らしいことですよね。 こんな素敵なことをくれたのは、翔太さん
That first live concert, that sound totally wiped me out. That is something really wonderful. The one who gave us something so wonderful was Shōta.
The last quote shows that こと can also be quite wonderful, not trifling or worthless at all. So what is the difference between こと and もの in くれたもの / くれたこと?
I would suggest (as in my original answer to you) that the use of もの indicates something that can be kept and treasured, as opposed to something that is simply an experience or action received. もの does not necessarily indicate something concrete, but it does indicate an 'entity' of some kind. That is, not simply a one-off instance of kindness or love, but something that is gained and can thus be kept. (I suspect that the use of こと and もの in 勉強したこと / 勉強したもの is similar. The first is simply the content that is studied; the second is what is gained from study. But I would be very careful not to exaggerate the difference here; in actual usage it doesn't seem to make much difference.)
It's possible that もの takes on the meaning of something gained and kept because もの refers to physical objects, but I'm hesitant about that explanation, because it is perfectly normal for もの to refer to non-physical objects. In fact, it's one of the dictionary definitions of もの: 人間が考えることのできる形のない対象.
I'm afraid I can't give you any more than this. I think you need to acquaint yourself with the full range of uses of both もの and こと in order to get a feel for them. The range of uses and meanings is quite broad, abstract, and in some cases overlapping, and it's hard to gain a grasp without a sense of all the possible usages and meanings. It's rather narrow to just focus on one rather particular usage and (in a sense) try to build a mini-theory of meaning based on that single usage.
I hope this is of some help to you. I'm afraid I can't give you any more. Perhaps a Japanese native speaker can give you a more definitive answer.
