What boat for a family circumnavigation?

What boat and why for family of 4 to do a circumnavigation on a moderate budget?

I am leaving the question somewhat ambiguous as in part my curiosity is philosophical as well as pragmatic.

I know there are several boats that could and have done it. I have read the 'Bluewater' lists and gone a round or two in a few of the threads but what I am trying to figure out is what is the best fit for us.

We currently sail a Martzcraft/Roberts 35. It could do it.

While we have cruised thousands of miles mostly coastal and like alot about her however for world sailing we are starting to consider whether she is perhaps not right for a trip around the globe. She is perhaps a tad small, as racers in a former life we also have to confess that she is not quick.

We would still prefer to go as small and simple as possible, but what is small, simple yet comfortable for living aboard for 3-5 years with school aged children?

Our plan is a'standard' circumnavigation but with the current Gulf of Aden situation it would most likely be via the Cape of Good Hope.

For the sake of a guide let's say 40 - 55ft.

Budget is very variable. In reality we will spend what we have to get the right boat. Say loosely 150k-400k.

Boats we have considered

Peterson 44/46
Stevens 47
Amel Super Maramu
Bristol 45.5
Hallberg Rassy 42/46
Brewer 42
Saga 43
Montecarlo 43

All advise and thoughts welcome.