The recipe I gave comes out like a stiff pudding. It is misleading with all the milk. It is thickened with corn starch. I would just add strawberries in one layer and use a stabilized whipped cream for the icing. Just search "whipped cream" on this site and you will find it. It holds for 24 hours.

There is also a "ultra stabilized whipped cream".

Another thought might be to search "Zuppa Inglese" on this site. It is made with cream/pudding, cake and whipped cream. It may be closer to what you want.

I think alot of these desserts are different with every person who makes it.
Maybe between all of these you can come up with something close.