A cabinet that tall shouldn't need a stack, just a hole with a rotary disc to control the flow, but in my experience with vertical smokers, I smoke with a fully opened exhaust vent to reach peak convection and flow.
Your cabinet is roughly 7 times the size of my SV-24 (6-1/3 cu ft), which has approx 3.5 sq in of exhaust vent opening in the top/center of the cabinet, but I have a removable 24" stack to increase the draft. You may want a 6" vent opening (18.84 sq in, if my calculations are correct, which is 5-1/3 times the size of my vent) for this cabinet, being approx 45 cu ft (minus wall thickness with insulation/double wall), and possibly a 18-24" stack. Your intake vents for the propane burner need to be close to the same capacity as the exhaust, with buffering (example: a box with two or more layers of side walls with staggered inlet holes and a ring around the outside with the primary intake on bottom, buffering on the inside of this ring) for windy conditions to avoid a flame-out condition from temporary down-drafts due to wind. Wind can cause a lot of problems with gas burners if the inlet draft is not buffered. With an elevated internal mount for the burner such as what you mentioned, instead of mounting under the cabinet, a simpler intake baffling system could be used with less issues. Possibly just a baffle plate under the burner to prevent a direct flow of air upwards form the the vent opening to the burner should be effective in reducing down-draft issues.
You may want to look at a few main-stream/commercially designed vertical smokers at your local venders to see how they built the burner/intake housings so you have a better idea what is going on with the lower end of propane smokers. The intake for propane smokers is the most important part of a conversion, IMHO. I haven't built any from scratch (yet) but have made a few conversions, and the intake for the burner and burner positioning were the only real issues I have ever encountered.
If upon test-firing you encounter issues with grate temp variances from top to bottom, this can usually be corrected with baffling over the burner, in specific, the size of the water pan, or additional baffling added around the top of the pan. If the pan is too small, it allows more heat to flow inward from the cabinet at shorter distances above the pan and creates higher grate temps on the lower to mid-level grates, with lower temps on the upper-level grates. If the water pan or baffle is too large, high temp in the top and low temps in the bottom will occur. Ventilation rates have some effect on these conditions as well, but seem to have far less effect as baffling does. The grate temp variances are more noticeable in taller cabinets, such as your 5-footer, then in a 24-30" cabinet. The taller the cabinet, the more precise the baffling needs to be to achieve low grate temp variances.
For the burner output, being it is insulated, a 50-55K BTU should do fine in most any weather, unless you want to smoke birds @ 350* in minus 40* winter weather, of course. It may take 45 minutes or more to reach stable temps when you fire it up in colder weather, but once it's hot, it should hold temps reasonably well. You can add fire-bricks or other thermal mass to the lower end later on, if needed. My uninsulated SV-24 can reach chamber temps of approx 400* above ambient temp without breaking a sweat, and it's a 20K burner.
Any other questions come up, or your need clarification on any of this, let me know. There is probably a vent sizing conversion per the cabinet size, but these figure will change based on the thermal insulation efficiency for your cabinet, so they may not be all that useful. If I find one I'll drop you a link.
Good luck on the conversion! I'm sitting here in envy of your warming cabinet find. Oh, the things I could do with a smoker of that size....and, it could still be kept transportable.
Eric
