If a transformer is unloaded it's very inductive.
If a transformer is fully loaded it's nearly completely resistive.
If you use a 8V 100VA tranformer with a 3.2Ω load the transformer will be very slightly overloaded so it will look like a resistor to the dimmer. A 100VA transformer is very unlikely to overheat if a 101.25W load is connected, especially in this case when most of the time the dimmer will limit the current.
If you add a snubber network and overrate the TRIAC, there's no reason why your dimmer can't be used to driver a slightly reactive load. I've seen phase control dimmers used to control the speed of universal motors before with no problems.
100W is a lot of heating power for a foam cutter, I doubt you need anything this powerful, a 6V 12VA transformer will probably give you enough power.
EDIT:
You'll need to increase the capacitor to 2.2µF if you want to reduce the resistor to 500R. If you can't find 5k, then it's probably more convenient to use 100nF and 10k.