No. Running cells without shutoff circuits in series is always recommended against. In any case, a single rcr123 even with a circuit should be enough to power that. The fact that it gets extremely hot tells me there is something else amiss. Perhaps even a short somewhere. Are the wrappings on all the cells completely intact?
I don't think there is a right or wrong answer for running cells in series. But ICR chemistry cells, the ones with the protection circuits are typically ones that can have thermal runaway if they short out.
IMR chemistry, while still containing huge amounts of power, does not tend to suffer thermal runaway. Most of batteries of this type do not have protection circuits and are normally higher performance batteries.
As that is a high voltage driver in that drop in, it may well not work with a single battery, as it is buck driver and likely requires 6v to operate. But the op would need to check the specs.
The LED itself, if it had no driver will happily work on a single Li-ion cell.
Personally I don't mind running multi Li-ion, but I prefer to run 2x in series over 3x.
It'd be trial and error, but the op might be able to run 2 x 16500 batteries instead of 3 x 16340, should work out to a similar length. But no guaranteed.
Op - as far as batteries go, I like the Efest IMR/INR batteries. Lots of info here on batteries:
http://lygte-info.dk/review/batteries2012/CommonSmallcomparator.php