The posts need to stay where they are in my opinion.
By replacing this area with a header, it needs to be supported to the foundation or a beam under the floor. So, no I would not remove anything without an answer from first, and the first one is where I would start,
1.Town building department- low cost, need to do for future sale anyway.
2. Engineer and bring stamped drawing to building dept, and still pay town fee.
3. Lumberyard, with small fee for drawing, and new material purchased to make a header, with posts to a supporting area under the floor.
I really wish it was easier than that , but if you do not spend the $$ now, how much more do you think you need to fix it later?
I inspect and see all sorts of handyman fixer upper redo's, and have been called in to fix a few after someone got in over their heads.
I hope this helps you to find the right answer,
Made in the