So I was out tearing apart my fence (hey everyone needs a hobby) and thinking about this while I did it, and here's what I think you I would if I could only make it one day a week. emphasis is on squats and OHP -
Week one -
{OHP - heavily, 6-10x3 start with 6 x3 and every week add more sets until you get to 10, then add more weight and start again
{Pullups - 6-8 x whatever. You don't want to go to failure on these so pick a # of reps you can do in between sets of OHP without killing your OHP performance.
Squats - 5-10 x 1-5 heavy
RDL/SLDL - 4-8 x 3-5
dips - 6-8 x 4
notes - the strict overhead press and pullups are supersetted to save time. Do OHP, then pullups then rest before the next set.
week 2 -
OHP - heavily, 6-10x3 start with 6 x3 and every week add more sets until you get to 10, then add more weight and start again
Deadlift - Heavily. I'd go with 5x5 or something similar
Squats - 15-25 x 2, 70-80% of your 1rm just for some practice and volume
{Close grip bench - 6-8 x 4
{bent over rows - 6-8 x 4
notes - close grip bench can be replaced by 2-3 board press (which should still use the same grip but more weight). I've yet to determine whether pullups or bent over rows are more relevant to upper back development for improving overhead presses, so if you think that pullups are better you can repeat the OHP/pullup superset from week one, or you could do a CGB/3BP superset with the pullups... whatever you think would work best for you.
All in all, remember this is a worst case scenario I think. If you absolutely cannot make it to the gym more than once this week, pick one of these two based on when you last deadlifted heavily, and go for it. but do try to get to the gym 2-3 times a week.
Anyone got any opinions or questions on the routine I came up with?
edit, there is a lack of core work. IMO it's low priority. yes, yes I know I know... I'm going to die a hideously disfiguring death for leaving core work as "low priority" but if it's such a big deal to you, do it when you get up in the morning. Grab your ab wheel, or a rope for some power iron coils, or do some situps, or grab something heavy and put it overhead for some saxon side bends or something. you don't NEED a gym to work your core, there's plenty of gym free ways to do that.