I find it strange that you think the landlord is going to trash your rental checks to use that as an excuse to evict you rather than accepting your rent money. There has to be way more to this story or you're completely paranoid.

Assuming there's any actual basis for your concern:

You can send it certified mail so it requires a signature upon delivery so you know it was actually delivered to the landlord. As far as the actual payment goes, get your bank to issue a cashier's check directly to your landlord and then film yourself putting it in the envelope with all the certified mail stickers, etc on it. If he signs for the delivery and then for some bizarre reason trashes the check rather than depositing it and then tries to initiate eviction proceedings that should be a pretty easy case to prove in court that you did in fact send payment and he received it.

No reasonable person is going believe that someone would get their bank to issue a cashier's check written out to their landlord to pay their rent, film themselves putting it in a sealed envelope, and then mailing that sealed envelope through certified mail requiring a signature on delivery and not actually send it. Especially when you can easily produce the bank records to show that the check was actually issued and that you never returned the check to your account.

I think a scenario of a landlord just shredding someone's rent checks so they can try to evict them unlikely as well, but less unlikely than someone doing all these steps to show proof they sent payment not actually sending payment. There are some shitty landlords out there. If it's a matter of them wanting to jack up the rent or something and they can't because you have a lease then it would be way easier for them to just not renew your lease when it ends than try to do a bs eviction.