Low Gear Jumping on Old Road Bike

[Eagle17]

I have an old Sovereign Free Spirit 12 Speed with friction shifters. It is a great bike overall except for one hugely annoying quirk that is has had since I got it, for free I might add. Since day one it has had this habit of wanting to jump out of first gear. It will do it no matter what I am riding on, flat, up hill or downhill. It does ti considerably fast when going up hill. The steeper the grade the faster it will jump. It generally jumps into 4th gear. I have had the cables replaced, new cable housings, and completely adjusted the derailleurs. I am at a loss as to where this is coming from and what to do about it. I really want to figure this out myself without paying a repair shop to do it, with questionable results. A couple of points of interest. I am certain the front derailleur is not the stock derailleur. It looks like someone took a standard derailleur off of and 18 or 21 speed (a three sprocket derailleur), removed the bottom sprocket and adjusted the gears and chain to run on the upper two sprockets. I don't know if this might be influencing this problem. Also, just today I discovered a tremendous amount of slack in the cable. when I try and shift into higher gears (i.e. if I try to go from 1st to 4th or anything like that). This might be making the problem worse but I doubt it is causing it. I doubt this because the same day the cables were replaced and tightened along with derailleur adjustments, this problem was still present.

A not on how the shifters work. They are lever shifters, on the center of the bike right up against the handlebars. To chance gears (From 6-1) you push the lever from straight up and down to laying flat against the frame. I can post a picture later if this actually proves to be relevant to the problem.

[nfmisso]

my first guess is that there is a chain problem; one of the following:
* one or more chain links are too stiff.
* chain is too long.

next guess is that there is not enough slack in the cable housing between the shift levers mounted on the handle bar stem and where they are clamped or terminated on the frame so that any movement of the handle bars causes an up shift.