94 Ply Acclaim, V6

I have a problem with starting my car. It started gradually, and now it
seems that I have to "turn over" the car 20 or more times every eight or so
tries. Today it started right up on a number of tries, 8 or so in a row.
Then a had a problem (many, many turns before starting) early tonight, and
then afterwards and later tonight it started the first try.There is a click
sound when it doesn't turn over. I have had the battery, alternator and
starter checked 2 weeks ago, and they seem to be ok. The starter wasn't
taken off to check for other things. The problem seemed to start 2 weeks
after I got my gas tank straps replaced. Maybe a coincidence. What "loose
"wires should be checked? If it turns out to be a solenoid in the starter,
do I have to replace with a Nippodenzoor or a Bosch starter?Any suggestions?
..

Thanks for any help! Peter.