I've have a later version TT, SMT 030, came up with the same things lately, not regarding the cartridge port, but bombs.
Kept the system pretty much dated, old HD Driver, NVDI, bla bla, normal stuff, no MiNT. Had an old Segate HD.
Haven't dug into it, actually packed it for sale. Noticed now and then it would bomb at boot.
Things I changed, went to V9 of HDD, installed a new NOS Segate 4GB SCSI internal disk (internal termination removed, external terminator in place).
I did have a SCSI to CF readier inside, stole that for the Mark X.
Has a GE Soft Fast Ram board, think 64mb of 60ns RAM, 8MB ST RAM board.
Using TT video port. Has a Maxon GAL programmer off the serial port.
Sometimes a couple of resets wouldn't do anything. Sometimes letting it set as you say, it would boot no problem.
Only noticed this at boot, thinking along the lines of where mzry is going, could be the powersupply.....