power - Alternatives to Large Transformer or PSU for Driving DC Heater

I have a 3D printer heated bed, instead of 3d printing I want to use it for reflow soldering. The bed is intended to operate at 70c, using 12v or 24v. It can be wired in series or parallel depending on the input voltage, it's 0.8 ohms wired in parallel, and 3.2 ohms wired in series.

I want to reach 260c, and the power demand will be at least proportional, so I think I'll need at least 90W * (260c-25c)/(70c-25c) = 500W. Lets say 700 to be safe. To push that through the 0.8ohm heated bed I'll need about 24v at 29A.

So that means I need either a large and expensive 24V PSU, or a large and expensive transformer.

But is there any way around that? For example, could I connect the heated bed directly to AC, and then use a triac to carefully ration the on cycles? I'm hesitant to do this because of the low duty cycle (15%), and high peak wattage (4.5kW).

Are there any other options? My first choice was to buy a cheap 30A 24v PSU on ebay, but that just blew up so I'd like to try something else.

Edit: To clarify what I'm asking: Is there a way to drive a high current, low voltage resistive load from 120v AC without using a transformer, or a full blown switching power supply?

Answer

Update: I've tested the solution I proposed and it does work.

So to summarize. I was able to drive a low impedance resistive load (3.2 ohms) directly from AC using a zero-crossing SSR at low duty cycles (<15%). This allowed me to pull 700W from mains without the need for a large transformer or switch mode power supply.

I included a 20A fuse in series to disconnect the load if the SSR fails. It didn't blow.

There was a negative side effect. The high peak current (over 50A), causes lights in the area to flicker.

I was prepared to just deal with the flickering lights, but ultimately my 3D printer heated bed failed around 240C (as mKeith predicted). I've since switched to a 1000W hotplate. It flickers the lights a bit too, go figure.