We used a travel cot downstairs. You can get ones with a bassinet in the top so it's not as far to reach down and put them in. We had the Graco foldlite lx
You could get a wooden playpen. They are like a crib but for play, bigger and have adjustable heights. They are very useful when you need a minute to do something and leave them somewhere safe. If you need something portable, maybe a travel cot like someone adviced above.
I bought a pack and play when my LG outgrew her Moses basket at 8 weeks old. It has levels so that she’s not directly on the floor and will last until she’s around 4. Can be used as a travel cot and a play pen when she’s a bit older (currently 15 weeks)
Travel cot or pram.
We had the SnuzBaskit and it’s longer than most Moses baskets.
My LG outgrew hers at 5 months as well. We have a soft blanket/mat she uses to roll on and she will nap on that supervised. Once she hit 6 months, we started naps in her cot in her room with the monitor on (although today it's too hot in there so she's currently napping on her mat)
Mine sleeps really well in the pushchair :)