I agree they should be matched otherwise one defeats the other.
Any new matched set of deep cycle batts will run the furnace all night . Keep the temp moderate and try to limit all other electrical things that draw from the batteries.
Some dept store deep cycle batts are really hybrids. Starting/deep cycle batts that have thinner plates .
Ex...Walmart Marine grp 29's are hybrids and they are getting lighter as the years go by. They were 67# and now weigh 62# , just be careful what you buy.
I use DEKA AGM 12v. deep cycle RV
8A31DTMthis link also offers some general battery info.
Bob