I'm not sure you need to go all the way up to 120 - when putting together this dissection, I worked to maximise all stick lengths, but if you accept that the lower bound is 41/10, you can shorten some stick lengths to give a denominator of 10 throughout (which, as a bonus, gives a simpler dissection).

Of course, this does mean that your program should probably be looking for larger denominators...

Best known dissection should be equal to 41/10:

Divide 9 sticks size 29:

4 x (41/10 + 41/10 + 41/10 + 41/10 + 42/10 + 42/10 + 42/10)
3 x (48/10 + 48/10 + 48/10 + 48/10 + 49/10 + 49/10)
2 x (49/10 + 49/10 + 49/10 + 49/10 + 49/10 + 45/10)

Reassemble as 29 sticks size 9:
16 x (41/10 + 49/10)
12 x (42/10 + 48/10)
1 x (45/10 + 45/10)