Your base probably needs to be a roasted squash puree, I don't think it will work well just being used to flavor a stock. Normally you would add cream to roasted squash to make a soup, but I guess that wouldn't be vegan. Butternut squash is tasty for this (and very autumn/winter), if you haven't actually picked out your ingredients yet.
If you want to add asparagus flavor, you should consider toasting/grilling the asparagus first. Applying a dry heat to asparagus when cooking it will bring out a very savory flavor (a nice addition to a vegan dish), but just boiling it in liquid will make it taste "grassy". It all depends on what flavor you want out of it, really. Asparagus is really a spring/summer ingredient though, if you're really wanting to be "seasonal" with this dish.
If you're boiling something rapidly, and it's not in a terribly deep, narrow pot, then essentially all of the heat output of the burner is going into turning water into steam. The latent heat of vaporization of water is 2260 kJ/kg, so if you want to reduce something by a volume V, and your stove has power P, the time required is:
t = V * (1 g/mL) * (2260 J/g) / P
If V happens to be in mL, and P is in W (J/s):
t (s) = V / P * 2260
This would be modified slightly if you're using a really tall, skinny pot, since the convection within the pot, from the bottom to the top of the liquid, would be less efficient, with more heat transferred to the sides of the pot and out into the air, but I doubt you're actually going to try to reduce something like that. The P here is the effective power; for example, a gas burner wastes a lot of heat out the sides, so the advertised power will be higher. See TFD's answer for approximate efficiencies.
If you don't know the power of your stove, in all honesty, the easiest way to measure it would probably be to just see how long it takes to boil away a given volume of water, and work backwards. To get an accurate result, you should not boil a pot dry - once the water is a thin enough layer, the heat transfer might start working differently, with the pot itself heating up more, and water splattering. So you could, for example, put in a liter of water, boil away at the stove setting you intend to measure until it's substantially reduced in volume, record the time, then pour it out to measure how much you boiled away. At this point, knowing the power output might be overkill, though; you can really just measure the time per volume reduction, and use that, unless you care about the power for other reasons.
Trying to deduce the power of the stove from, say, the temperature of an empty pot or of the burner without a pot on it (assuming it's electric) would be difficult; you'd have to deal with the heat transfer between metal and air, and the convection in the air.
Dependence on ingredients shouldn't be significant - you're still just boiling water, unless there's a substantial amount of alcohol, in which case the latent heat of vaporization will be different. Pure alcohol has a latent heat of vaporization of 841 kJ/kg; I haven't found a good table for mixtures.
For solutions, as I noted in the comments, the latent heat of vaporization should be that of water, plus/minus the heat of solution of the solutes (I forget which direction that's measured in). The most common solutes are probably salt and sugar, which have heats of solution of 70 and 16 J/g, respectively. (I found this table, and converted.) The next most common thing I could think of that might be present in substantial concentrations is citric acid; this paper reports a heat of solution of -57 J/g. In all these cases it's small compared to the latent heat of vaporization of water, so pretending the liquid is water should be a good approximation. It's possible that things change if you're reducing really far: heat of solution does depend on concentration. That is, things are different thermodynamically (statistical mechanically?) in a nearly-saturated sugar syrup than in slightly sweet water.
Best Answer
Very simply, all of them work.
The major driver of what tastes good to you is expectations. If you are accustomed to eating soup with a certain taste, and expect it to taste that way, then any time you prepare the soup with something different, it won't taste good to you.
But there is no rule to define that some liquids taste good as a soup base and others taste bad, universally. And without knowing how you like your soup, it is impossible to predict which ones you will like personally.
Update In the edit you mention that it is the concentration that is wrong for you, not the flavour profile altogether.
What gives the soup flavour is not the liquid part. In fact, the liquid in both sauces and commercially available "soup base" as well as fond, stock and other similar stuff is pure, tasteless water. The taste comes from whatever is dissolved in the water.
Whatever you are using as a soup base seems to be just much more concentrated than the sauce. It is very probable indeed that one of the things which don't have enough concentration for your taste in the sauce is salt, another one is probably MSG. But also other flavour bearing compounds are probably provided in less concentration in the sauce. After all, the sauce is supposed to be poured over solid food, and shouldn't taste bad when you lick it off the food surface, it is at a concentration which doesn't taste too bad when it comes in contact with your tongue. The soup base is at a concentration which after dilution falls in the commonly acceptable range (but at a lower concentration than undiluted sauce).