Quick tiramisu with many restrictions
I think that it is doable, if the restriction doesn't require the dessert to be exactly a tiramisu. 

Many dairy-based cremes are interchangeable, similar in texture, and require no eggs at all. The alcohol in some tiramisu versions can be safely left out. The short time is the worst restriction. Thickeners like agar agar may not set in the short time. 

You should start with buying prepared lady fingers, as you can't bake them so quickly, and it is probably too much effort anyway. You can use any tiramisu recipe for the moistening liquid; if it includes alcohol, just leave it out. You can add a few drops of alcohol-free rum essence if it called for rum or another hard alcohol, or a fruit aroma if it called for a fruit liqueur. If it only specified coffee liqueur, leave out the liqueur but use normal coffee. You might want to use instant coffee dissolved in water instead of just-brewed espresso, because hot coffee will interfere with the short chilling time. Then you need the dairy creme, and you can finish with the traditional cocoa powder. 

For the dairy creme, you have to choose one which will hold its shape without thickeners. You can add agar agar or carrageenan or the calcium-sensitive type of pectin, but don't trust them to turn a runny mass into a firm one, the time is too short. Use them as an insurance, and hoping that you will get something which gives some resistance to being cut or chewed, as opposed to being just scoopable. Whipped cream together with Greek yogurt is not a bad idea; other cultured milk products can work too, if they are on the firmer side. I have had similar desserts made with just schmand as the filling, but they stayed overnight so some whey could diffuse into the non-syruped cookies, making the cookies softer and the schmand drier. If you have access to the type of modified starch which will thicken without having to cook (for example sold as "cream stiffener", but also as a cream replacement product to be whipped with milk), using some of it may help. Don't use liquid sweeteners like corn syrup or honey, stay with sugar, and separate the whey from the yogurt to get a firmer result. 

Another way would be to use a starch thickened pudding instead of a custard. This is a more common substitute, but normal starch has to be cooked to a boil, and will require longer chilling. You may be able to pull it off, if you make the whole dessert rather flat and wide, use a pre-chilled vessel and dip the ladyfingers into cold liquid, and then put the poured dessert into a freezer for a quick chilling. It will need quick work (so lots of time remains for chilling) and frequent attention so it can chill without freezing. The first version is probably less stress. 

Whichever you choose, such a major recipe change is not easy. Make a prototype at home before you cook it for a crowd, so you can catch the major problems in an early version and relaxed environment, and then you will know if it is doable for sure.