Re: 59 Bassman Reissue sounding kind of harsh...
I am not sure whether you are still checking the thread, but I think a few points are worth considering. The first is that the Bassman has a very specific, bright tone. From you original post it sounds like you understand and are ok with that, and are concerned that it has moved from bright to harsh. Some of the people responding, however, are making suggestions which would basically alter the fundamental character of the amp. If you do not like the Bassman tone, fine, but there is no point in making a bunch of mods to try to make it sound like something that it is not. It would be better to simply find an amp whose tone you prefer.
Ok, with that said, now for the nitty gritty. With respect to the tubes, those who are telling you that the fender, factory tubes stink are dead on. Most new tubes are pretty crappy. There are some good boutiques tubes, but the best (power) tubes to my ear are the JJ's. Also, biasing can make a huge difference, and, as noted, there are biasing mods which can make this an easier task on this vintage circuit.
Preamp tubes are a totally different issue. I do not know why you would buy new preamp tubes while you can still get old american made tubes. Whether they are truly "NOS" which are rare and expensive, or just used (in which case their values are usually tested and identified), in general they are going to have a much finer tone (smoother, less harshness, richer overdrive) than any new preamp tube. As for the 12Ay7, that is a very low gain tube which will give you more headroom. You can use a 12At7 which on the gain spectrum lies between the ax7 and ay7. That makes a lot of sense for a guitar player looking fora a responsive blues/classic rock amp. Use the ay7 to keep it as clean as possible.
You can also find older american made power tubes. They are expensive, but awesome.
The tube rectifier, while not cheap, will fundamentally change the character of the amp and move it toward the more classic Bassman tone. The tube rectifier responds to drive and has tonal characteristics which are wholly unique. Google it for more specifics. As an alternative, Weber makes a solid state rectifier which makes the tonal characteristics of a tube rectifier. It will not necessarily resolve all of the brittle tone issues, but it will give you natural compression and a pumping, classic tone.
With respect to the speakers, it is again important to remember that old Fenders had a very bright tone. The speakers do wear in, but moving away from that brightness for a tweed amp is moving away from the fundamental tone of that style of amp. There are speaker alternatives which some people tonally prefer to to the Jensens (which are very unlike the old classic Jensens, starting with where they are built). Weber, again, makes killer alnico magnet speakers which sound like vintage speakers, in more than one price range. They also offer options to alter to tone of the speaker. Really, for the money I think they are the best speakers made today. Made in the USA, great options, great service, great price, great tone. How great - the new Fender custom shop totally hand made ERic Clapton amps are using Weber designed speakers! When and if that is a change you want to make, that is the way to go.
As a final note, the guitar choice can make a big difference. High output pickups, especially ceramic magnet pickups, are going to compound the original brightness of the circuit, and probably take things to a more brittle and sterile place. Alnico magnet pickups, which all vintage pickups used in various iterations, are going to retain more of a sweet ringing tone without seeming harsh. The difference in tone can be huge. Standard series fenders, for example, use (at least as of last time I checked) ceramic magnet pickups which do not come close to the tone of good alnico magnet pickups. You can also get a noise reducing peddle, such as that from Electro Harmonix, which will really tame any single coil noise and help the amp sound as good as possible.
Good luck!