In Fender blackface and silverface amps the pre-amp really doesn't distort much, so you really need to look at the power stage regarding headroom issues.
I would get your amp working correctly before undertaking any modification. If your filter caps are originals, get them changed. Trying some JJ 6V6s is also a good idea, as is checking that you have a 12AT7 in the PI.
I'm not a big fan of the Jensen reissue speakers (and believe me I've see lots of amps with them in). They all seem to sound fairly harsh, and are not cheap either. As a general rule Alnico speakers have less head room than ceramic speakers, so I would definitely look to replace the speaker in your amp. Weber make excellent speakers, however you would need to import one from the US. Banzai Effects in Germany sell Weber speakers, but at highway robbery prices. I really don't know how you can justify charging 135 euro for a $30 speaker.
If you did go with Weber, I would recommend a 12F150, although it would be worth contacting Ted Weber for advice on this as he is always very helpful.
I have had good results with Eminence speakers in the past, although their current range is rather bewildering, and I am at a loss to recommend anything from their current range. Bear in mind that lower power speakers are generally more efficient due that higher powered speakers.
Silverface Deluxe Reverbs are one of the most desirable Silverface models, so think twice before you undertake any mods to your amp, and make sure that they are reversible and well executed. I have seen some horrific hack jobs. Don't pay someone to do this to your amp.
Hope that this is helpful.