Calculating Capital Gains/Losses when selling multiple Bitcoin UTXOs on an exchange

Lets I am mining Bitcoin and receive a payout to my wallet at the end of each day from a mining pool:

Day 1: 0.1 BTC (BTC Price on receipt: $50,000)
Day 2: 0.1 BTC (BTC Price on receipt: $29,000)
Day 3: 0.1 BTC (BTC Price on receipt: $55,000)
Day 4: 0.1 BTC (BTC Price on receipt: $15,000)

I am aware that since this bitcoin is from mining it is taxed as income as soon as it is sent to my wallet (this is kind of besides the point of this post but mentioning it anyway because it also helps determine cost basis):
Day 1: 0.1 BTC (Taxed on: $5,000)
Day 2: 0.1 BTC (Taxed on: $2,900)
Day 3: 0.1 BTC (Taxed on: $5,500)
Day 4: 0.1 BTC (Taxed on: $1,500)


Now lets say bitcoin is at a price of $65,000 and I want to send 0.2 of this bitcoin to an exchange such as Coinbase or Gemini to sell for USD (another taxable event). Since Bitcoin has a concept of UTXOs this is where the confusion is coming in for me.

I would naturally want sell the UTXOs from Day 1 and Day 3. So when building the transaction to send to Coinbase or Gemini I manually select the Day 1 UTXO (0.1 BTC) and the Day 3 UTXO (0.1 BTC). I believe this is where the different accounting methods such as FIFO, LIFO, HIFO come into play. In this case I believe I am using the HIFO (highest in first out method) method because it would benefit me the most. I am also aware that once an accounting method is chosen it should be stuck with.

I just sold the 0.2 BTC on an exchange that was created from a UTXO (0.1 @ $5,000 cost basis) and UTXO (0.1 @ $5,500 cost basis).

Since Bitcoin was $65,000 at the time of the sale, this means I would receive: $13,000.

Is this the correct math to do to calculate capital gains (Combining both cost cost basis of each UTXO) ??
$13,000 - ($5,000 + $5,500) = $2,500 GAIN

Am I looking at this correctly? Lets say I am not keeping track of the cost basis of each individual UTXO in my bitcoin wallet and I go to send a whole bunch of them to an exchange for selling. Do I have any other options here? Or is it a must that I know the exact Cost Basis at the individual UTXO level (whether it was mined, received as payment, or received from a friend). Also, what if I accidentally switched up the way I hand picked these UTXOs for selling throughout the year. One time I used FIFO, one time I used LIFO, one time I used HIFO, etc… Am I in trouble here?