Using a pic for making a simple 100 Hz oscillator ?
...because OP has them on hand, they have a built-in, factory-trimmed RC oscillator stable to 1%, and OP already tried to use a 555 (albeit not the TLC555) and it was unstable, again using the parts OP had on hand.
Yes, your solution uses more parts and requires quality caps, and even then may not be better than a few percent accurate. And it won't be as stable as a crystal, like you claim. Plus an analog input of the PIC can be used to make a temperature compensated oscillator, if needed.
More components?
01 x TLC555 or equivalent
01 x 4049B
01 x 0.1µF condensator (c2 is not essential)
03 x resistors (if trimpot is not used and replace with ajusted resistors)
PIC:
01 x PIC12F675
01 x 0.1u bypass cap
RE: LTC6991 - nice part, but $3.80???
The PIC12F675 is $1.26. I wouldn't use that part in a design but OP has it on hand. I would use the cheaper 10F200 at $0.68 for an oscillator like this.
The TLC555 is $0.87, the cd4049 $0.51, the 60ppm precision thin-film cap might be $0.50 to $0.70
[ edit: I always quote 1 off prices here rather than 100 or 1k because often the OP is making less than 100 anyways, and the relative pricing is still clear using 1 offs ]