Yes I use LDOs all the time. That is what they are designed for.
There are plenty of TO-220 options available.Watts, I hear you about the +/-12. About the TO92 package, on Mouser it looks like they can only supply 100mA. I may be reading datasheet wrong but assuming I'm not, is 100mA enough?
Without a load the filter caps will charge to the peak voltage of the transformer output minus the voltage drop across the diode, which in your case should be about (17.8vac x 1.4) - 0.7 = 24.2 vdc. Pretty close to what you are measuring. Looks good to me. There will be next to no ripple without a load as the only ripple would be due to the leakage of the caps.
I have several antique generators from the early/mid 1940’s which are rated as 110v output. The “hook it up to 110” May be a hold over from those days but obviously well before PL’s days. They use reverse current relays in the DC section as aliens hadn’t crashed yet allowing the reverse engineering of semi conductors...Was it really common to have 110 VAC 40 yeras ago? I've never seen anything specified for 110 in the U.S. 117 and 120 yes. 9 out of 10 electricians "hook it up to 110". Was that just something that was handed down?