Hybrid 1ph/3ph load center fed by rotary phase converter?
Yes! It can be done.

But it's fairly tricky.  L1 and L2 are a single phase which is center-tapped for neutral.  It is not possible to bend it to an angle other than its natural 180 degrees.  But it is possible to disregard neutral entirely, and treat L1-L2 as a single phase. And use them as two corners of delta configuration.  The rotary phase converter synthesizes the third corner of the triangle: L3, which is 240V from L1 and L2, and all in correct phasing.

This can be overlaid on the existing L1 and L2, so it does not need to be a separate service. Note this diagram is the rotary phase converter's perspective.  What happened to neutral? 


source: installation instructions

Neutral remains exactly where it started: halfway (120V) between L1 and L2. This is asymmetrical: L3 is coincidentally 208V from neutral.  208V will not be available unless the rotary phase converter is spun up.  This arrangement is called "Wild leg delta".   Since L3 is the "wild leg", it must use orange wire or be marked. (NEC 110.15**). 


source: Wikipedia

Use a panel meant for 3-phase wye

So the panel will have a separate neutral from ground bar**.


To connect a 120V load, use a single breaker placed on L1 or L2, and neutral.   
To connect a 240V single-phase load, use a 2-pole (240V breaker) placed on L1 and L2. 
To connect 240V 3-phase, choose any 3 spaces. 
To connect 208V single-phase, use a single breaker placed on L3, and neutral. 


Breakers need to be listed for their voltage, which means 125V breakers will not do in 208V slots.**

3-phase cabling should be done either with THHN/THWN-2 in conduit, or with /3 Romex -- with white wire re-marked as a conductor (good choice for orange, since then you only have to tape one wire).   

If you are wiring something made for 240 wild-leg (seems unlikely) which wants 120V, it can be derived by carrying a neutral along too; for that you'd want /4 or /2/2 cable. You would have to  be very careful about loops and biases in connecting that - you could end-run around those issues by installing a small 240-120 transformer for its control power: install it on L1-L3 and that would assure the machine could not start up unless 3-phase power was on.

There's no particular difficulty in complying with Code with this setup, so there is no reason not to do it.  The only shortcuts are either trivial (orange wire) or dangerous (omitting ground). 



** I presume OP's rejection of Code is merely because he does not want to be thwarted; and he is willing to comply when it's easy.