I believe that this would be possible, but you'd set it up the opposite way around than you've specified. You'd set the central database as the publisher, and you'd use Merge Replication.
Merge Replication includes an option to allow dynamic filters - so what you'd want to do is set the filters up so that each subscriber only receives the rows that it originated - probably by adding a column to some of your tables to include the HOST_NAME() of the server where the row originated. You shouldn't need to do this to every table, because once you've filtered one table, you can have cascading filters that filter out rows from additional tables using joins.
As to "incremental fields" - I assume you're talking here about IDENTITY columns? Luckily, these have also been thought about - basically, the publisher manages the IDENTITY range, and hands out smaller ranges (of 1000 values, by default) to each subscriber.
Caveat - these are the general principles, but I haven't tried this kind of setup myself before. I'd recommend that you try it in a "toy" database first, and try to get it working.