Hi
"... I know that I position the cursor near the end of #3 then "PLACE ON SEQUENCE AT CURSOR", but that always seems to split either #3 or #4, resulting in an extra clip of 1 or 2 frames"
That's because you are placing the cursor "near" the end of a clip. The cursor won't "jump" automatically to a join between clips and consequently this results in a splt and insertion which can be a few frames out.
What you should do is...
With your two (or more) clips on the timeline, grab your new clip from the media list and drag it down to the timeline (don't release it). Now as you drag it right or left along the timeline the end of the yellow clip delineation box will "Lock onto" any join between clips it passes over. Release your new clip at the point (the join) you require. The clip will neatly insert itself between the clips in question. No gap is created unless you decide to delete the inserted clip afterwards.
Nat