Sorry I'm working night shift this weekend so not really able to respond quickly.
That might work, but you're going to have a ton of ripple. My opinion is to use a 3.3V LDO regulator. There are lots of options and they can be very cheap, a simple 3-pin regulator in a TO-220 package, a bridge rectifier and two capacitors and you will get a perfect 3.3V output no matter what the fluctuation in your wall AC or the number of coils active (keep in mind current draw on the supply will change depending on which output is selected).
Fixed output LDO regulators are very easy to implement, you just need to read the datasheet and application notes.
Here is an example using an LT1085 3.3V regulator from Analog Devices. This one is on the more expensive side, around $10, but most from Texas Instruments, Onsemi etc. are around $2, this is just the one I found the LTSpice model for quickly.
LTSpice operates in peak voltages, so the input is 8.48Vpeak which is 6VAC RMS. I used 1N4007 since that's what you have on hand, but you could also use a all-in-one bridge rectifier, or even Schottky diodes which will have a lower Vf. The green trace is the input voltage at C1. The dropout voltage for this particular regulator is actually on the higher side, around 1.3V. That means the voltage drop across the regulator must be at least 1.3V or the regulator will stop regulating properly. That means the trough of the ripple at the input (green trace) must not be less than 3.3V + 1.3V = 4.6V. For that reason, C1 must be relatively large to keep the ripple low, the reason I used 1000uF. The 150uF output cap is per the LT1085 datasheet to ensure output stability.
You can see the output trace, in blue, is very low ripple, a perfect 3.3V and it will be 3.3V no matter how many coils are being used as long as the input voltage never drops below 4.6V, which it should not even with a sag in your wall AC of even 10%. In this example, the regulator is dissipating around 0.5W, which is fine for a TO-220 package, might add a little clip on heat sink.
So anyway, that's my $0.02 on how at a high level I would implement a 3V supply for the coils of a relay switch.