Your cross bike probably has a head tube angle of 72 degrees and 45mm of fork offset. This gives it 65mm of trail and 20mm of front wheel flop:
Your Swift Folder has the same figures (72 degree HTA, 45mm of fork offset), but the wheels are only much smaller. This drops the trail to 45mm and the wheel flop to 9mm:
If you wanted to make your cyclocross bike handle like your Swift Folder you'd need to need to grossly redesign the front end. 74 degree head tube angle and 60mm of fork offset is close:
To change the Swift Folder to behave like the cyclocross frame you really should have much less fork offset. 15mm is getting you there:
That is a drastic change, removing 30mm of fork offset. The curve in the fork blades would be almost immperceptable.
Personally I like road bikes that have around 40-45mm of fork offset like your Swift Folder. However they require wider tires to handle well. This is one of the reasons that I like the Avocet Fasgrip Freestyle on 406mm wheeled folding bikes. It is a wide tire (around 40-42mm) that has low rolling resistance and runs well at moderate pressures (I'd run it at around 50-60psi). It is probably as fast as the very narrow tires (like the Conti GP3000) that many people like to run, but greatly improves the handling of the bike.
The other thing that helps low trail bikes is to carry the load on the front instead of the rear. Folding bikes are good for this anywhere since there is typically a lot of space between the top of the front wheel and the handlebars.
The mistake is that folding bike manufacturers almost universally try to copy big bike head tube angles and fork offsets instead of modifying them for the small wheels. For some people (me) this works out well because we like lower trail bicycles. For the skinny/high pressure set with rear loads it is a big mistake.
I don't think that trail and wheel flop define everything about handling. The smaller wheels make other differences too. I'd still like to see greater experimentation and study of small bike handling than what appears to be out there.