We have a client who owes us $5100. Our limit for small claims court is $3000. What''s our best legal route for collecting the full amount?

There is probably no good option to accomplish that. To prosecute for the full amount,  you'll need to engage the services of an attorney, which will likely cost you more than the difference. Most of the time, with claims of this magnitude, it makes sense to reduce the claim to the small claims maximum and go that route.