I am curious why the humidity is changing so much inside the screen printer, is there a heater or large flow of dry air into the printer?

A good approach my be to understand the root cause first. Have you talked with your equipment supplier about this?

Of course if all else fails you could add a water bath or damp pad. There are also some very nice little ultrasonic fog generators used with desk top ornamental displays. There are also commercial units you can purchase.

The solder paste needs to be robust enough to withstand fluctuations in humidity without drying out / slumping.

Increasing humidity inside the printer could cause slump / bridging during reflow.

Typically water-wash pastes are more prone to dryout / slump as they are hygroscopic. No-Clean pastes would be more resistant as they are non-hygroscopic.

Check with your Solder Paste Printer Manufacturing Company, they may have a fan or A/C unit built into the system to cool the operating mechanics and electronics of the printer.

If this is the case, this might be the cause of your paste drying out. You might need to attach a deflector of shield near the paste bead to protect it from this airflow.

Some of the older generation pastes were more susceptible to drying out in low humidity environments and slumping in high humidity environments. This was especially true with water soluble pastes.

Over the last few years we have seen most pastes formulated to withstand lower and higher humidity environments. In the case of water soluble pastes we now have a number of products on the market that are water washable where they have some ingredients that aren't completely water soluble but have surfactants that are able to allow the water to wash away the residue.

This has led to water washable pastes that are less hydroscopic. Also on the No Clean front there has been a change to higher boiling point/low evaporation solvents. This has allowed for pastes to have greater open and abandon times.

Typically these new generation pastes recommend a RH of 25-65% so both your printer and facility would be within specification. My suggestion is to look at the paste rather than increasing the humidity in the printer.