> there will be varying voltage drops if the load current fluctuates
Enough yaky-yak. Bcarso, off the floor.
What IS the load current?
Two to four op-amps is 3 to 20mA.
The lowest-Z Accutronics coil saturates at 28mA peak. This will be around 10mA of DC in the op-amp or booster driving it. They tell you not to saturate because it gets muddy. With normal speech/music peaking at 28mA, the caps can handle those peaks and the raw supply only has to be good for about 1/5th of that, or 2mA average DC. However, Fender guitar is a popular application for spring reverb and can have low peak/average ratio (clipped plucks and compressed sustain), so split the difference, 5mA maximum DC current due to load.
So a couple low-power opamps with no signal might be 3mA. A quad of hungry opamps driving an 8Ω coil might be 20mA idle, 25mA rocked-out.
This is not a large current or a large change of current.
We have a "12.5VAC" transformer. It is probably at least 0.3 Amps, and we are only asking for 0.050A AC, so it is more nearly no-load than rated load. At no-load it will rise maybe 20%, to 15VAC. Peaks are 15V*1.4= 21V. Diodes drop 0.6V, we could have 20.4V peak on the first caps. Ripple is well under 0.1V, so we take the DC as 20.4V.
The smallest load, 3mA, will drop less than a volt in the 220Ω resistors. Problem: this is 19.8 volts, in excess of normal chip ratings. I assure you that 99.9% of "36V" chips will take 40V for a very-very long time, probably longer than the spring's useful life. Or you could use 5532 chips, which are rated 44V, eat more current and will suck-down to 18.7V, and can drive the 28mA coil rating without boosters. Also low-noise, which can be an issue for the pickup end of the spring.
Or you could up the 220Ω resistors to (20.4V-18V)/0.003A = 800Ω (use 1K).
The largest load, 20mA-25mA, would drop 4.4V to 5.5V in the 220Ω resistors, giving 16V idle, 14.9V rocked-out.
The drop from no-signal to full-signal, a volt or so, should not affect chip opamps. The drop is symmetrical. These chips are not fussy about rail symmetry or voltage as long as they can pass the signal swing. The low-Z coils only need 0.224V drive! Even with a build-out resistor, only 1.3V. As long as the chip has 5V of rail-power, it will be fine. The hi-Z coils could need 13V drive, so we might barely miss "spec" with a 14.9V rail and some losses, but the rated drive current is not a precision thing.
The ripple is doubled with this half-wave contraption, but we just have to double the capacitance to "fix" it. At ~470uFd~1,000uFd 25V, double the uFd is much less than double the price, and far cheaper than another transformer (a second 12V or a 24VCT for true full-wave). Yes, it is 120Hz (per rail) and more annoying than 60Hz ripple, but the second R-C filter knocks that down a lot. Using rough math, I get 1 milliVolt on the rail and 1 microVolt in the chip. That won't amaze fans of super-regulators, but in a REVERB application I bet you have more than 1 microVolt of room-buzz on the spring pickup. (If you do suspect power-ripple, like when you unplug it the buzz vanishes in the second it takes the caps to discharge, use a separate chip for the pickup amp and give it a 3rd R-C rail filter.)
If you like regulation, aim for +/-12V DC from 12VAC windings. 15V DC is far too close to the 17V-21V DC you will get from 12V AC.