You're right that it's a very tricky situation. And feelings can lead one astray as you noted.Sense, feeling? A feeling there exists more to life?
I've found feelings not trustworthy. Not that they are wrong but by themselves they are not enough to justify a belief. So while I may feel that your position is wrong, that feeling alone doesn't justify a belief that you are wrong. I would need collaborating evidence, IMO, to justify it as something to be believed in.
IOW while what I choose to believe may not itself be fact, it should be supported by some facts. The more the better obviously. That's just how I see it. I not saying it as something you need to accept.
But the best the intellect can do is to ask questions and construct theories such as: Either there is an ultimate meaning in life or there is not. If life does not have an ultimate meaning and purpose, then any sense of meaning is just accidental and fleeting.
If life has an ultimate meaning, then the question becomes why does it have an ultimate meaning? And how does what goes on fit into the realization of that ultimate meaning? And how did that ultimate meaning come to be part of the universe?
This can go on and on with questions leading to more questions. That to me is enough to convince me that the mind can't answer the question because there's an unprovable root assumption somewhere along the way.