Absolutely. Just continue with regular weekly water changes. No need to alter the routine, or as Simon said, add additional water changes to the routine.
Unfortunately, as long as you are using tap water, the lowest pH it will get is what you have from the tap. 7.4/7.6 as you mentioned above.
If it gets down to 7.4, that should make a difference to the shrimp. Especially if GH is around 4.
As you say, the figures are coming down but that means the TDS and GH are getting too low really for cherry shrimp so I wouldn't keep doing extra water changes over your normal routine until you have a definitive plan, stick to your weekly usual for now. Make sure new water is added sowly as well!
You could continue with the tap water but would need to get some GH+ to bring the new water TDS and GH up, but thats a bit impractical if you plan to transfer to RO water soon anyway as that requires a different remineraliser.
With the RO water you will need to get GH/KH+ before you can use the RO water! The RO water remineralised is the safest way to get and keep the ideal water parameters as tap water can change from different areas and at different times of the year. As JayC mentioned, you could collect rainwater in the meantime but that would still require GH/KH+ I expect otherwise the TDS and GH (and KH) will drop even lower?
You will be able to check the TDS pen with the RO water as it should be 000 (or very very close) TDS.