IME and as online sources say, when a component is in circuit, you can sometimes get faulty readings. If it reads 'bad', it's bad, if it reads 'good', it could still be bad.

I've had issues where the associated diodes (buzzing flipper coil when held engaged) and transistors (controlled lamp never lighting) read 'good' but after replacing them, the issues were fixed. With all the other standard general fixes you list you have completed, if this locked-on relay is the only thing left with an issue, my money is on either the coil's diode or more likely the associated driver board transistor. Also check the associated driver board resistor.

You mentioned you have a new Swemmer driver? Swemmer's products are top of the line as far as quality and modifications from OEM designs (e.g. socketed IC's on the driver). I have a Swemmer 8TB MPU and never had a problem. BUT, even if the board is brand spanking new fresh out of the anti-static bag, a problem could have worked its way from the relay to the driver and blown the transistor. Happened to me with a lamp socket on my new Ni-Wumpf driver board when I accidentally bumped one socket leg to touching the ground when powered on. Before removing the transistor from the board, it tested good on my DMM. Replaced the transistor and lamp works perfectly now.

Was the issue there before replacing the boards?

Components in circuit will not give as accurate readings as they do when removed from the circuit. With the board being new, unless something went wrong and caused the transistor to fail, it's probably not the transistor. But I kind of hope it is for the fact that it is so easy to replace. The hardest part is waiting for the part to arrive in the mail!

Very interesting. My curiosity is definitely piqued on this thread.

One of the very nice features of Swemmer's board. My Ni-Wumpf has LED's only for solenoids, but I definitely have had times where I wished every transistor had LED indicators like the Swemmer.

On the OEM 80 driver, Q48 only has three traces: one to the edge connector, one to the associated resistor, one to the ground circuit.
Shouldn't be anymore or less.

There is no website for Swemmer. He is a pure "for the love of pinball" hobbyist. If you poke around here or youtube you can find him and send an email if you have questions. He is quite helpful.

I don't know if this applies to sys80, BUT with the original 80 drivers in sys80B, lamp numbers and associated transistor numbers were all off by one (e.g. lamp 47 was transistor 48). On the Ni-Wumpf board, they corrected the number system so that lamp 47 is transistor 47. IDK if Swemmer uses the Gottlieb original number assigning or if he straightened it out like Ni-Wumpf. If you think Q48 is the transistor for your relay because the original manual says so, maybe on the Swemmer driver it is not so. I really don't know, just trying to offer up my experience.

I think really, contact Swemmer esp. if you bought the board directly from him. If you bought it from Keith at Ksarcade.net, contact both of them. They both have excellent customer service. They may not be able to completely diagnose and solve your problem but they at least will be able to tell you some helpful info for diagnosing it yourself and hopefully you will be able to determine if it is the board or something else.