Never see the one you want before. I think there are reasons to design in that short of period. Otherwise cranking too long for every ignition probably damages the gear of flywheel.
Instead of searching long period ignition, maybe you should do a tune-up to short the cranking time.
If you never fix car before, it's wise not to do it in cold winter.
They could be a long list depends on the condition of car. Do a search about "tune-up" in this site, you probably find the list.
You can go to the garage for the price, If the price is too high, it is not worth do it just for remote-starting.
Good luck