There is a door on the Hexamid, a zippered screen door.
I had a ZP Hex. Horizontal rain was not an issue keeping gear dry inside away from the tarp perimeter. That's what the side beak and smaller footprint ZP add on bathtub floor were designed. Additionally, when it rains heavily and especially if it wind driven or a wind will likely present itself, the typical suggestion is to place the full rear back panel into the wind. There is also some slight adjustment ability in the ZP Hex in lowering the side walls during wind driven rain. This can slightly affect floor space. Lastly, and I don't see it being used in your Hex in Cali? set up, is adding a bathtub removable floor which was, I found, a useful add on with the Hex if wet conditions or wind driven sand were expected... and I still desired cross ventilation to reduce/avoid condensation. I also liked it was removable and I could do a different flat ground sheet when conditions were more in line to that approach. The sides of the "tub" helps prevent water from sheeting across a flat ground sheet and from ground splashes. A tub is more "idiot" proof.
I don't know if still can get a Hex fitting ZP Bathtub removable floor as the Plex has replaced the Hex. I do see them offered up FS used on line occasionally. And the Plex has a sewn in floor. Notice the Plex has a "split door" to the ground. What that tells me is that others were having this splash issue. WHY? IMHO, it could be purchasers didn't understand the design and optimal usage...likely as they rah rated with others on the UL/SUL ZP Hexamid bandwagon...an issue many NB ULers make, ME TOO...underestimating UL design and functionality while overestimating or ignoring their/our own abilities.
Another possible approach, although not one I'm always keen about because it can decrease ventilation, is to cut to shape a slightly larger flat footprint than how you typically set the Hex up. You can let the flat sheet creep up around the perimeter to avoid splash and sheeting.
Yet another way to avoid splash and sheeting across your floor is to prop up the perimeter slightly. I typically utilize flat lying trekking poles, small rocks, appropriate length branches, etc under the perimeter of a flat ground sheet. Propping up one side of the flat floor can work if your site situated on a very slight slope anticipating downhill direction of heavy rain. You have to be mindful of not damaging the incorporated Nanaoseeum floor though! The incorporated nananseeum being damaged/torn and Hex too short length for my height and stretched out sleeping position were probably the two biggest reasons why I abandoned using the Hex. I don't care what anyone posts on their site or says. Using a nanonseeum next to the ground and ground cloth over it will reduce the life span of nanoseeum possibly resulting in functionality issues of the Hexamid shelter.
Here's another suggestion. You said you have very light use on your Hex. From your pic it does indeed seem to be in good condition. Resale value of ZP gear including the Hex still remains relatively high. THAT MAY NOT LAST INDEFINITELY! You could sell it in the good used condition at a good price and roll the do re mi into a ZP Plex. People are hungry for ZP gear! Here's why this can make sense. Even if you do find someone to retrofit your current Hex with a DCF door based on the financial costs you already have invested in the Hex PLUS the retrofit costs, which for DCF can be pricey post production and considering the original manufacturer will not to do the work, it can possibly entail a greater overall costs than a new Plexamid.
Hope this helps providing options.