I have mixed opinions towards Torch. I've used their reflow oven, and it works great*, but on the other hand, their manual pick-n-place is just garbage, worse than a pair of tweezers.
*: temperature profile is extremely inaccurate with integrated temp sensor (~40C lower), so a K type probe attached onto target PCB is a must. They supplied one, and there is a K type probe socket on the front panel.
This unit seem more complicated to learn than anything else..However, I am still a novice at his stuff and have never tried batch soldering.
KL27X post #9 Seems to be really good.
Now this is just some ideas. those more experienced will be better able to comment on these ideas.
1st, using a toaster oven reflow unit would cost less. There are pizza size units which when converted would allow you to reflow large batches of PCB's
2nd, a lot of people built those DIY units and many have admitted they just do not use them. even their oven is too small, I am sure someone would be glad to send you the programming unit they made cheap..That project became a kind of craze..I have 3 toaster ovens, but never got around to building the programming unit.
3rd, Mikeselectricstuff has a video on how he built and uses a DIY device that uses a kind of SMD paste solder injector and a foot switch connected to a compressor so just just places the tip of a pad. pressed his foot and bam the solder is there. he demonstrated how quickly he could use this DIY jig..I think you could adjust the amount of solder for the thr0ough hole.
4th, regarding KL27X suggestions, before I read it. I was thinking a brick or ceramic slate that can take the heat, maybe use a Dremel tool to cut the grooves as KL27X described (my thought...Pizza brick in the DIY Toaster reflow oven)
Lastly, I have seen these "solder pots" that I guess you fill with solder and, do you just dip
the the underside of the through hole into is..Hot solder wicks up, I don't know about this but I have always wondered what those solder pots are for.
It seems to me with the number of boards, and the number of components, no matter what there will some trial and error. Maybe getting one of those solder wave machines are worth it and do not cost that much.
These are just some suggestions, take what may work,or maybe they will give some ideas of other ways to do your project.
Cheers!