... Should I use the 6x5? ... The circuit is just going to be a champ because the OT is SE ...
You're fine with a Champ, though a 6X5 is less capable (70mA) than a 5Y3 (125mA).
... Different tube rectifiers have different limits on how much capacitance the first filter cap they feed can have.
Info at this link indicates a limit of 16uf on the first filter cap, for a 6x5gt:
...
On the other hand, the data sheet linked on that page gives a 32uf limit. ...
... reel to reel PT and 6x5.
Mine are from a Webster Chicago 2010 which used a 35uf as the first reservoir cap.
I have also heard that you can fuse the secondary side of the PT for protection.
It's mostly unhelpful to think of the situation as a "capacitance limit" because you're stuck with vague "rules" from a variety of sources & anecdotes of "I got away with a larger cap." The problem is "the right way" to think about it is a difficult design-problem.
6X5GT data sheet (https://frank.pocnet.net/sheets/093/6/6X5GT.pdf)
5Y3GT data sheet (https://frank.pocnet.net/sheets/127/5/5Y3GT.pdf)
Notice both sheets describe a definite d.c. milliamp limit, but start getting fuzzy on a.c. plate current with reference to rating charts.
Caps suck current to charge to the applied voltage. If there is zero resistance in-series, the cap charges near instantly (http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.html#:~:text=The%20charging%20current%20asymptotically%20approaches,of%20a%20time%20constant%20RC.), but pulls near-infinite current. Your rectifier tube just popped. The higher the capacitance and/or higher PT voltage and/or lower-resistance, the higher the charging current. Rectifier = Popped.
So in accordance with Ohm's Law, we can reduce the current pulled through the rectifier (which is one of the "peak a.c." limits) by either lowering capacitance and/or increasing the series-resistance. Or we can lower the a.c. voltage delivered from the PT, though usually we picked that because we needed a certain d.c. voltage output.
The PT's winding resistance is part of this "series-resistance."
So the resistance of the PT (as well as the internal resistance of the rectifier) tend to bring the cap charging-current down. And we don't always have specs on the winding resistance of the PT we use. Where larger filter caps were used in vintage gear (and the PT's resistance didn't limit the current enough), designers added a resistor per-rectifier-plate to reduce the charging current & protect the rectifier.
So any filter cap limit is a fuzzy rule-of-thumb. The problem is rectification is non-linear, so mathematically predicting peak charging current is a pain. The Radiotron Designer's Handbook 4th Ed has a chapter devoted to rectification, and copious charts/graphs to work through to predict the needed external resistance (if any) for the PT, a.c. voltage, desired d.c. voltage, load current, and capacitor µFs.