I have two transactions which have remained unconfirmed for over 24 hours. I've tried rebroadcasting them but it seems not to be working.
Rebroadcasting does not increase your priority.
If there are any miners here, can anyone help me out and try to manually drop these transactions so that I can retry with a higher fee? Heck, if there are any miners here who can push both these transactions through, I'll gladly send you $10 in Bitcoin for the help.
Those miners now want $10 in fees for that same small transaction. Miners can only confirm transactions, they can't drop them.
Check
https://btc.com/stats/unconfirmed-tx, required fees for a fast confirmation are 14 times higher than what you used. Best option is to just wait. If you're very fast at the right moment, you can add them to
https://pool.viabtc.com/tools/txaccelerator/.