I would repair the amp to use the proper capacitors and 5AR4 tube. The voltage drop / lack of headroom / early distortion of a 5V4 might be good for guitar but not bass. There are some things that you can try first though.
Re-solder all the connections that were made when the capacitors were installed. There should only be one ground point, at the end of the ground bus at the input jack. As this is the only ground point, make sure that the jack contact to the chassis is free of corrosion and that the jack nut is tight. The caps should not be grounded to the chassis. If there are any grounds in the power supply there will be a ground loop and hum. If there is a cap can, it needs to be isolated from the chassis with a cap can washer and not in contact with the metal. This is a common mistake people make when re-capping.
Pull the rectifier tube and clip in a set of diodes. Use two series 1N4007 or equivalent on each leg of the high voltage tap. Like this
this. This will help you determine if the larger capacitor/5V4 is causing a problem.
Converting the heaters to DC is not necessary. This is a very quiet amp as designed. You could unhook the heater circuit and inject DC as a temporary test to see if this is the source of your hum.
If the speaker cable was removed and replaced with a jack, the jack needs to be isolated from the chassis to prevent a ground loop. The speaker return should not be grounded to the chassis. There also needs to be an isolating washer on the ext speaker jack. Not having one on the ext amp jack is normal.