First look at primary side vs secondary side.
1 to 1.5 volts drop while on is a small % of line voltage compared to secondary side voltage.
In primary side you have smaller currents and less heat generated in Trac or SCR
You also have much less power loss from these.
To get a good spot weld, you need to keep all secondary loses low and have a very low resistance path.
So keep it simple, on primary side the trac or scr will just need to survive primary side current while secondary is shorted, much less.
You stated a microcontroller, when done correctly the analog part can be very simple.
First step is better data about your microwave oven transformer.
With out this data, you are just guessing on currents. The secondary short current during spot weld could blow the house breaker.
The power line is dangerous so use your 35 Vac supply to get some facts.
Just need some simple tests with good facts.
As I asked a few posts ago
A series resistor to primary winding with you measuring some Vac values.
Source voltage, Resistor voltage, primary voltage, secondary voltage.
Do two sets of measurements for each series resistor. One with secondary open, One with secondary shorted.
Start with a resistor with higher resistance as too small could harm your 35 Vac supply.
Need to see some change between open & short for all but Source voltage.
Source voltage should be close to 35 Vac but will change due to load.
Even with this data it will still be some of a guess as to what will happen at 240 Vac.