A few thoughts that might even add more beauty and Romanitas to this beautiful chapel:
1. Add a tester over the altar to unite the altar and dossal curtain into a whole and align to the traditional rubrics around this.
2. Where possible even a very slight predella is also very desireable. In circumstances like these, they might not be particularly high, but even a slightly platform helps to distinguish the altar from the rest of the space.
Evidently there are practical questions here about the height of the ceiling in this particular space and whether these elements are possible -- however, one possible workaround if space is tight might be to "cheat" the tester back so that it does not obstruct the priest. As well, any predella here would evidently have to be very slight, amounting to likely no more than an inch in height. For it I would recommend the same red material and galloons used for the dossal and tester.
How might this all look? Here's a quick digital mock up:
But as noted, these are simply suggestions to add additional beauty to an already beautiful and edifying private chapel. Very well done.