I've been reding this post and having a good laugh. Years ago in my go-kart racing days I ran one triple. What a PIA. It worked but it was **** on wheels. We ran 3 horizontal engines each with its own chain setup to a live rear axle. If one engine hesitated, the others dragged it along. Bang, that is the sound of the pistons and part of the connecting rod coming through the case. Didn't always explode, but did a happen a couple of times. We ran them in parallel and did get it to work (sorta). I would never attempt it in series with engines like that. Do the math, the slightest rotational misalignment will result in massive shaking. Alll the power needs to go through the bottom engine crank. Heck, these engines snap there cranks all the time when mowing just by hitting a rock with the blade. I do not believe a Rigid connection as recommended above will work. I would say you need a connection where the engines drive the load(s) either separately as recommended above or in parallel via connections with a limited amount of slip. Even better to devise a setup where the engines can "freewheel" and only pick up their share of the load when they are up to speed and the load demands it(slip clutch). Rather like syncing a generator to a power grid.
And BTW, back when I was a kid (and I'm still a big kid) I hacked together many contracptions and left my fair share of blown apart parts on the ground. Also when the thing you are proposing comes apart, I suggest it be surrounded by a steel shroud to catch the shrapnel. I still have a helmet with pieces of an old Merc Hurricane embedded it in from an old hydroplane.
One final thought, I don't believe that "phasing" of the power pulses will be an issue. Just connect them together with something with some give and a slip clutch and wind them up. They'll each pick up their share of the load when the time is right.
Have fun, and take pictures.
Andy