I am not sure what type of injection system I have but it definitely is
fuel injected. I too think (am hoping) it is technique related,
certainly the least expensive route to a solution. I am leery of
burning up another starter while trouble shooting technique. My
un-preheated cold weather/cold engine starting technique is very
similar to my warm weather/cold engine technique and is as follows:

throttle open 1/4 inch
mixture full rich
electric fuel pump/prime on
wait a few seconds (2 at the most)
crank

In warm weather it starts right away. Colder weather takes 4-5 seconds
of cranking before it starts. Cold weather takes major cranking and no
fuel pump after the first attempt. Sometimes I get it going and
sometimes I don't. Both engines are very difficult and uncertain,
although the right engine is much more cooperative than the left.