Greetings Mike-- yes your are on a path that will function. You didn't mention what frequency bands the tri-band operates. You will find that amateur radio has many many bands and modes. I'll assume you are probably talking about a 2 meter (144-148Mhz), 1.25 meter (222-225Mhz), 70cm (420-450Mhz) frequency modulated (FM) tri-band radio which are popular.

Your attic mount sounds quite functional. The thickness of the steel plate is not important. At VHF-UHF frequencies, the RF only travels on the very outside of the skin of the metal a few molecules thick, thus it only needs to be thick enough for support the antenna. However, it does need to be large enough to create a good ground plane that the antenna capacitively couple to. Thus the minimum radius from the center (where you put the antenna) needs to be at least 1/4 wave length for the lowest frequency band. For a 2M/1.25/70cm antenna that would be about 20 inches radius. A 45x45 inch square of thin sheet metal would work fine. Larger is fine, smaller area creates losses and an uneven radiation pattern (same on a car roof).

Very little will radiate below the plate. This is good. You don't want to radiate your family. At 45 watts not a big problem, but you license lets you run 1500 watts so you don't want to cook yourself. Also, you want the RF energy to go outward, not be wasted warming dirt or house wiring.

A couple other thoughts on attic mounts. Hopefully your roof doesn't use any type of metal layer in the roofing. I've heard of a copper layer in roofing blocking signals, but I don't think it is used much. Also, VHF/UHF signals are VERY line of site, so high, outside "base station" antennas, fed with very low loss coax will always work better. But we all have to compromise to real world and an attic antenna is much better than many solutions.