Wiring nema 5-15 to L14-30?

My small generator only has 5-15 receptacles with common 120v output and I
need to wire this to a L14-30 receptacle on a transfer switch to provide
120v power to both sides of the switch so I can use all 10 circuits. I
don't see a problem with this but I can't find anything about it after
many hours of searching the web. So what I plan is to use 2 120v outputs
from the generator and just double up the neutral and ground and then put
each hot lead on the separate hot leads of the the L14-30 thus giving the
same 120v to each side of the transfer switch. The generator is only 2300W
max, so I'm sure there won't be a problem using 12 or 14 AWG scrap
extension cord (SOJT 600V) for this. I'm trying to confirm I'm not missing
something. The generators ground is not common with neutral and the
transfer switch is a Connecticut Electric EGS107501A. I've already wired
the switch in and it works fine from the line side. Just need to get the
generator side hot.

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