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From what I am reading, there are 3 attested tandem drivetrains:

1) crossover drive, with timing chain on the left, and main crankset and drive chain on the rear right. This seems to be most common.

2) Crossover drive, but with the main crankset and drive chain in the front instead of the back. This uses a very long drive chain, but has lower frame flex and better chain line.

3) Right side drive, with the main crankset on the rear. Right side drive has low frame flex, low weight, and low width.

What seems to be missing is:

4) Right side drive, but with the main crankset in the front. This would seem to combine the width , weight, and flex advantage of right side drive, with the chainline advantage of front-crossover drive. However, I have never seen it.

I'm building a tandem with no front derailleur, And I'm concerned about frame flex and weight. I'm thinking about trying it. I will just use small sprockets for the sync chain and a larger sprocket for the front/drive chain. Will it work? Anyone ever seen this done? Any problems?

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    It is likely that at some point in cycling's history, everything we can imagine has been tried, although I've never seen this. I don't see how this would be an advantage over the #3 configuration. If you set this up with triple cranks front and rear, with the granny gear for the timing chain, you could get a decent chainline in the back and avoid interference between chains. – Adam Rice Mar 11 at 14:34
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I suspect #4 doesn't exist because it makes the stoker's position hard to get power out of.

If you have one very long chain on the RHS, with the chain passing over and under the stoker's chainring, then there is minimal tooth engagement on top, and perhaps none at all underneath. Certainly not the "toothcount/2" teeth engaged on the front wheel. This would make it very hard for the stoker to get power down.

A solution might be to use some jackwheels, like jockey wheels but to press the chain down around the stoker's chainring to give more tooth engagement. But this would add complexity and potentially jam up.

Since you only want one chainring, cheat. Have two at the rear, and one at the front. Power the rear mech directly off the larger chainring, and use two smaller equal-sized inner chainrings for the timing chain. You could even use 1/8" chain for the timing chain, and use 3/32" from the stoker's chainring to the cassette/derailleur.

In hindsight I think my suggested solution is similar to your #2.

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    Your suggested solution is identical to #2 indeed. Which does work, but I anticipate chainline problems. #4 still will have a dedicated, separate timing chain between the front and rear. But the main drive chain goes to the front. So the stoker has only one chainwheel (one for the sync chain only) and the front has two chainwheels (one for the sync chain and one for the drive train). I have seen the front BB used for the main drive before, but only with crossover-type drive. – BetterSense Mar 11 at 14:15
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    @BetterSense yep - I'd be concerned with how to get the drive chain back past the stoker. Plus you're now carrying a couple metres of additional chain, and chain is suprisingly heavy. – Criggie♦ Mar 11 at 19:34

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