You're going to have to say how this will be done but I'll go with what I'd expect:

If you're using a HD wallet with a derived xpub and xprv then you merely import the xpub into the server for the clients to pay into and keep the xpriv on an offline device...

You'd then sign a transaction with the xpriv and transfer it to an online device to consolidate everything.

The actual signing of the 1000 inputs into one transaction is trivial and will be handled by any client. The important thing is, if you don't need to consolidate quickly, you should consolidate at a 1 sat per byte fee where possible and enable a rbf double spend in the software you're using.