So is it a medium swaddlebees OV you have? My DD is 23 months and has been in large nappies for a year probably! She is not a heavy wetter but i dont think a cotton MEOS would last very long on her either
and swaddlebees are just cotton velour too, so although they're soft and organic, they're not very absorbent.
Weenotions Northern lights are very absorbent, and if you're not looking anything fancy then they are a good price
or upsy daisy nappies (although i havent tried any yet) would be too. They have a good resale value too so if you're not going to be using them for very long you wont lose out!
If you have any pocket nappies, i can recommend bluberry inserts and they are easily boosted if needed. again, weenotions pockets are very reliable, as are bumgenius nappies.
Have you considered using wool over fitted nappies instead of wraps? Much better resistance to leaks, and Ive hardly used wraps at all over fitteds in the past 6 months because i love the wool so much! and a pair of longies or shorties can be worn long after a child has PT!