Welcome to AK!! We were all newbies at one time!
Hope you will find some interesting reading and discussion here.
In regards to your problem, there are a few possibilities and some questions for you based on your description and your picture.
1) If you originally had the can cap, all the grounds were at the same place, namely the chassis surrounding the can cap. If you ground one 20uf cap at the original ground, that's probably ok. The dual 40uf's being grounded at the ground PIN connection of the 6BQ5 is probably the culprit. This is because the two grounds are not necessarily at the same common lowest ground potential, and this can set up a ground loop which can cause hum. Because I don't have a schematic, I can only generalize - I'm assuming you're working in the B+ power supply here. I would try putting the ground back directly on the chassis as close to the original can as possible and see whether that solves the problem.
2) A couple of things from the picture that I'd comment on. - With what looks like vinyl electrical tape holding the two caps together, I can't clearly see the polarity markings on the caps or the values. Electrical tape, especially in warm or high voltage situations can be unreliable to hold for long and leaves a sticky residue. I'd recommend desoldering, cleaning the exteriors and then repackage them using tie wraps to hold everything down. Looks cleaner that way and much more structurally sound.
Also, at least from the picture, is the right side blue cap (+) side down? If the lower right hand corner is the 6BQ5 you were talking about and you are connecting the cap to the GROUND lug of the tube, that may be reversed polarity. I'm not sure since it appears the upper part of the picture has the (-) side of that cap being grounded to the old can chassis ground. If this is correct and the (+) side of the right cap is supposed to be handling high voltage from the tube socket (B+), then you should better insulate the (+) lead of the cap, it looks perilously close to the chassis and one slip and its bye-bye cap and probably transformer.
So we'll need some clarification here as to what's going on and how you've wired these in. Also, if you are replacing the old can cap, you should desolder the connections to the old cap and recreate the circuit using your new caps. Not real clear whether you've done that.
Hope that's a first step in your trouble shooting.
Regards,
Bart