Tru-Cut mower question

Just got a used Tru-Cut 25" commercial C-25 H10 (10-blade, Honda GX 160 engine) mower and wondered if someone out there has one of these? I called TC to get a manual, but it had nothing about the engine or the throttle lever mounted at the base of the handles. So I downloaded the engne manual separately, but it doesn't seem to be the exact engine and of course doesn't reference the mower's throttle. WHat I want to know is how I am supposed to set everything to start and run the mower properly... when cold and when warm.
Here is where my confusion lies: the engine has a petcock (fuel) lever and a choke lever, which are self-explanatory, but then there is a throttle lever on the mower itself up by the handles. At the top of the mower's throttle lever's range is "STOP" and at the bottom, "CHOKE". This lever manipulates an entirely separate arm or lever down on the engine that is just above the engine's designated choke and petcock levers.
So when I have the mower's throttle lever pushed down to "CHOKE" that has nothing to do with actually setting the choke... right? I am just supposed to put it there with a cold engine, set the choke lever on the engine to closed, open the petrcock (obviously)... and start it? Then as the engine warms, back off the choke lever on the engine, and .... as to the throttle lever on the mower.... ? Move it to the halfway point between STOP and CHOKE?
Cause here is the problem... when I move the choke on the engine to the position the manual says it belongs in (once the engine is warm).. to the "OPEN" position, the engine races as if the choke is ON... but if I place it all the way CLOSED, then when I engage the thumb-button drive to self-propell forward, the mower barely goes.... I need the engine idling faster. So with the throttle lever on the mower halfway between STOP and CHOKE, I placed the choke lever on the engine about 1/4 from CLOSED. The mower ran good that way but I am not sure it's the proper way to run the engine....?!!
Anyone??? TIA!!

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