https://www.mouser.com/Wire-Cable/Hook-up-Wire/_/N-5ggs?P=1yx5jmeZ1z0jnf6Z1z0juksZ1z0xfpoZ1z0x8gx More than $0.20 per foot is just plain nuts. At $1.90, even more nuts.
Some basics about wire:
a) The OEM Dynaco products came with vinyl-clad, tinned solid 22 gauge wire for the most part. And for the most part, that will do fine in most applications.
b) Yes, vinyl insulation will turn into a sticky mess if not soldered properly.
c) Because 1. The iron is too cold & 2. the solder in use is not a Eutectic mix & 3. the proper technique - what to heat first - is not being used. One, two, or all three.
There is no need for boutique wire. Mil.Spec. wire is fine, and will very certainly serve the purpose if one wishes to use a belt, suspenders and Velcro. BUT! Two things about PTFE insulation:
i) It requires a very sharp stripper so as to cut the insulation but not nick the wire.
ii) PTFE in the environment is very nasty. And if burnt, even small exposure to vapors will kill birds and damage cats. So, save the cuttings and dispose of them so that they will not be burnt - such as in trash-to-steam.
A few more things, while I am on this particular path:
Insulation ratings were created for raceways, conduits and point-to-remote-point wiring conditions. Not for internal wiring within devices. And the point of all of it was so that wiring carrying a high voltage would not cross into a lower voltage line within that conduit or raceway. Now, with that in mind, consider that the typical tube amp has operating voltages from 5 V to ~500 V. with the base of the rectifier tube carrying both 5 V and ~350 V. The potential fault here will be more towards a solder bridge than an insulation failure (vs. melt-down).
Which leads to a real concern I have with stranded wire in such applications. A loose strand could cause genuine havoc.
Which leads to a real concern I have with solid wire - especially wire that is not properly annealed prior to insulation. Even a small nick during the stripping process could cause a weak spot that could fail subsequently.
A perfect example of not being able to have it both ways. Writing for myself, I prefer solid wire (and very sharp strippers), and why I advocate checking _EVERY_ connection when taking on a new-to-me piece of kit.
NOTE ALSO: Wire colors have meaning. Mixing metaphors can be dangerous. https://www.radioremembered.org/xfmr.htm Try not to use a wire color that does not, at least, resemble what its common use meant 'back in the day'. Using white or green wire to carry active current is a bad idea, as both colors have specific meanings (here in the US anyway): White = neutral or return, Green = Ground. AND! All secondary windings on transformers carry current, which is why you will never see an RMA-compliant transformer showing a green lead - unless it is to the shell - not uncommon. For our Euro friends - here are all the color-codes rolled up: https://www.allaboutcircuits.com/textbook/reference/chpt-2/wiring-color-codes/
What all this comes down to is: Be careful out there! There is no rush, and whereas there is always time to 'do it over', that very nearly always takes longer than doing it right the first time. And, if technique is important, skills applying said technique comes with time and practice. Give yourself the time until it becomes second-nature.
Enjoy!