My folder is a Tern Verge X30h. I bought it specifically for the speed. It has the SRAM dual drive which makes up for the 20" wheels. My daily ride is a Kona Jake ( my commute is a mix of gravel and pavement) and the Tern is a faster ride on pavement. I bought a folder for exercise when on my frequent business trips and so I didn't want a commuter but something to get some speed.

The dual drive is definitely the key to this. Unfortunately this is significantly above the OPs budget.....