Your definition of 'work' is wrong. Take the example of prisoners who worked tirelessly to build the rail roads in the US; by your definition, they did no work, since they weren't paid.

'Work' is simply energy expended achieving a task. And by that definition, your proposal cannot be a proof of work, since no work is done by doing nothing.

Further, your idea of having block producers hold stake as collateral does nothing to change the inherent security model of the system; attack cost will still be a constant in the amount of stake, vs true POW where attack cost is super linear in the number of blocks produced.

If you really want to stick with proof of stake, I have suggested before that simply auto electing the top N staking block producers ranked by their stake will resolve the problem of voter apathy, which is the true failure mode of DPOS.