ok. I will admit I don't know the exact specifics of your machine because I have never seen one except in pictures, but in general I would highly caution against this plan because it is potentially dangerous. Forcing the intake burn draft vacuum from the intake end makes it no longer a vacuum, but now a pressurized situation where combustion gases could, in the event of poor draft (for many different reasons beyond your control) push their way into your living space and kill you. Much better would be a similar setup electrically, only leaving your intake as it is and install a forced DRAFT inducer in the flue pipe (controlled by your described electricals). I have seen these in action, and although it seems they might require a bit of maintenance (never used one myself) would be very effective and FAR SAFER.
There is a potential for problems here as well though, because your unit if like the newer ones, probably has a barometric damper installed in the flue. You will wanna speak to someone knowledgeable in setting up solid fuel systems in homes about the potential problems to your system on installing forced DRAFT inducers in flues with Baro damper, and just how to do that if its even possible. Key questions here would be. is it possible? should it be positioned above or below? and does the baro need adjusted accordingly to the new system? I would think you might even have to eliminate a baro to run forced draft but not sure. all this stuff is key to your safety however. so dont experiment with this without doing your homework first
Another thought... have you ever actually had your draft checked out? Perhaps you have a baro that is set improperly that fixing would solve a lot of your slow firing response problem. The forum has a loaner program for these (manometers). I would think from burning the hand fired appliances I have, that with coal, youre going to need some patience, but not familiar with all that complicated automatic stuff to know for sure.
One more thing to consider. Relocate your thermostat to a place that is closer to the floor or in a cool pocket in your home but that gets good warm air when your plenum blower kicks on. this might get you the fire you need sooner, but not overwarm the house... might take some experimentation for a little while with thermometers to find just the right spot tho.
Lastly... can you bump up a size in coal and stay within your appliances guidelines? larger coal may also help. It would depend on your firebox and grate. larger coal MAY do nothing for your problem.
I think, but not sure, that the only appliances I have ever seen FORCED INTAKE on, which is what youre considering, are OUTDOOR furnace or boilers, where it would not matter if there was firebox fluegas leakage until draft caught up. Inside the home you DONT WANNA GO THERE.
I do know one methiod of providing instant heat for sure. Have it here at my place. OIL
but we dont wanna go there either
Hope this helps.