What's wrong with shorting a Tx to ground? I've never done it on a SAM board but if Stern support says it OK then why not.
Simple test, game on, coin door closed - alligator clip a wire to ground strap inside the backbox and touch the metal tab on the Tx for a split second.
If the coil fires you know the coil is good, the voltage is good and wire connections are good. But then this means it is a board issue, probably the Tx.
If it does not fire it is either voltage, wiring or coil. Touch the tabs of the other pops. On Whitestar LOTR they are Q9, Q10, Q11