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[CriminologyProf]

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[LoyceV]

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/.

[DoooV]

I accelerated 4c61b92a81d88499b1eb642f3d2939be1af7e847aa3cbaecb14e96eaee8c894b using ViaBTC tool

No need to pay me

You should try next hour for your other tx : https://pool.viabtc.com/tools/txaccelerator/
And you should put higher fees next time

[HCP]

... I've tried using Mycelium's option to bump the fees, but am told that I have insufficient funds (which is not true).

Just to clarify... The "Bump Fee" option (aka. "Replace-by-Fee")... can ONLY use coins from outputs which are generated in the transaction you are trying to increase the fees on. (This applies to ALL wallets that allow RBF)

Your first transaction had outputs of:
16hUPiK8Q7ZXYAqUZdoDsqVkq249jkyXmR - (Spent) 0.01073038 BTC
14WoZyqvowrn3rFTxLdVNNSdTyH2mXphjP - (Spent) 0.0051 BTC

I'm assuming you were sending 0.0051 BTC... and 0.01073038 BTC was the "change". Under normal circumstances, you could have elected to use some of this 0.01073038 BTC to bump the fee (NOTE: you can't use any other coins from your wallet, even if you had 100 BTC in your wallet... you're limited to the coins from the transaction output)

However, as you had already "spent" the change of 0.01073038 BTC from your first transaction by creating and broadcasting the 2nd transaction... you had nothing left to bump the fee as those coins were spent (even if not confirmed)

You MIGHT have been able to bump the fee on the 2nd transaction assuming you had not spent whichever one of these outputs was your "change" from the 2nd transaction:
1GXDWPUzbZYHYc3HUT39V4ydysRmPXXncB - (Spent) 0.0091 BTC
1B56iMVo5oejJq4Z5adE5eW3HWLcdYF5Nx - (Spent) 0.00155019 BTC