What's wrong with doing an ACH transfer for amounts of more than $4,000? Most large banks seem to have limits of $25k/day for those transfers and that can be increased pretty easily (at least on business accounts). There usually aren't any fees for those either.
You must be quite rich. Every account I've ever seen limits ACH to $4,000 unless you have at least $100,000 in the bank, and then they will up it to $25,000.
No not at all, not even 2 months rent in my bank account. Maybe try some different banks? My only experiences are with Chase, Marcus and a very small town bank.
