If I were in your position I'd look for an alternative flight plan that suits you and check-in whenever but make sure you go immediately to the gate once you are through security. Register with the gate agent that you are prepared to be denied boarding, they'll then either tell you there and then or ask you to come back just before they start boarding. If they decide to accept your offer you can tell them what flights you want to be on rather than them choosing your new routing. The gate agent for sure won't know in their head all the options.

As to compensation if you voluntarily decline to fly the agreement is between you and the airline but were they to have to bump someone without there agreement, the figures are for cash (but they may offer you vouchers against LH flights which will be for a greater value)

More than 3500km, Up to 4 hours delay €300
More than 3500km, More than 4 hours €600

and a seat on the next available flight plus telephone calls, food and overnight hotel if necessary.

and finally if the flight is a 3 class configuration, they might choose to invite you up the stairs, especially if you've offered to help them out but not if you turn up at the airport looking like a bum Good luck, I love being VDB