Specifics on rolling over "late" 401k contributions

After I had to roll over my 401k recently, my former employer made 2 more small contributions to it for some reason so those checks have been mailed and made payable to me (minus the 20% withholding). It seems simplest to me to just deposit those checks in my bank and then make a single contribution to my IRA from my bank for the full amount of the 2 checks (+20% tax). Is that OK? I don’t see how this would adversely affect the "paper trail" since I could show contribution(s) into IRA for the exact amount of the distributions shown on future 2020 1099R. If it somehow helps the "paper trail", I could do a contribution for each check.

If I MUST send the checks to my IRA company instead (and then make a separate contribution from my bank for the 20% tax) to satisfy IRS rules (I couldn’t find specifics on just how funds must be rolled over other than it must be done within 60 days generally), they have conflicting information on whether to endorse or not. On one 401k rollover page it says, "Note: If the check is made payable to you instead of us, mail it to us within 60 days to avoid paying potential taxes and penalties on your savings. Please endorse the check."
On another 401k rollover page it says, "Note: If the check is made payable to you instead of us, mail it to us within 60 days to avoid paying potential taxes and penalties on your savings. Please don’t endorse the check."

It makes more sense to me that I would have to endorse the checks since they’re payable to me, but hopefully I can just do what I want instead since it would be far simpler.

ETA: I did ask the IRA company the same question and they gave the unhelpful answer of you need to ask a tax professional so here I am. LOL