... I don't want all the time soloing gone to waste, so I'm waiting for that first block.
It doesn't work that way. Each hash is a completely new attempt. If your average time to find a block is (say) 23 days, and you haven't found a block in 22 days, your average time to find a block is still another 23 days from that point onwards.The average still holds, because sometimes you will find a block in less than 23 days.
But any work you've done without finding a block has already "gone to waste". You don't work your way towards some solution. Instead, millions of times each second, you throw away the previous work and try another solution to see if it's a good one.
