ok, a few comments here and there to clear up some things.

i once read what i think is a very good, persuasive article as for why type II sums of squares is better than type III sums of squares, especially if you're interesed in exploring interactions. it is:

ØYVIND LANGSRUD. (2003). ANOVA for unbalanced data: use type II instead of type III sums of squares in Statistics and Computing, Vol. 13, 163-167

so i guess at the very least you should try both type 2 and type 3 sums of squares and see what comes out. most people in the literature ignore this issue, however. type-3 sums of squares won the battle of sums of squres (there're actually 6 types of sums of squares) when SPSS was programmed because (a) type-3 is their default method and (more importantly) (b) it is the default method because it's the most likely type to give you statistically significant results. and we both know how people just luuuuuuv those p-values below .05 rite?

i went to that webpage and reviewed what they said. please, be very careful with the way in which they use the language. when they say that "technically" ANOVA needs at least 2 measurements per cell, the point they're trying to make is that you need at least two points to get a mean and deviations from that mean. it is kind of hard, as you can imagine, to deviate from yourself when you're the only score there. however, they were just trying to make a technical point with that. such small cell sizes should never be advisable.

with regards to the 0-cell count that also took me by surprise. they are right though, but i think the author of that post was a little bit careless with regards on not citing anyone (i mean, 0-count cells? that's a HUGE claim to make). i found a good article that addresses the issue in:

Searle, Speed, and Henderson (1981). Some Computational and Model Equivalences in Analyses of Variance of Unequal Sub-class Numbers Data in The American Statistician, vol. 35, 16-33.

the mathematics in this article may be well outside of your are of interest, but the conclusion is a huge IT DEPENDS. for instance with your particular case, if you had 0-cells in the boy level of the gender factor but none on the girl-level and wanted to make claims about your location factor (crossed with gender), you can do it. you cannot claim much about any gender effec because of that 0-cell there. it just gets too complicated.

now, on to your case... with regards to using ANCOVA i guess the only recommendation would be to make sure that you're not missing too much data in certain sections of the covariate. for instance say you have quite a few people on the group of ages from, i dunno, 15-20 years old, then not so many on the 20-30 group and then once again more on the 30 and up, ANCOVA is going to overfit and you're very likely to get significance as a statistical artifact rather than because of a real effect.

missing data is going to be a concern of yours regardless of the interactions or main effects being tested. if it's missing, it's missing and it's going to screw up something somewhere. now, i like those new numbers i see in your tableslittle bit better because they are not as unbalanced as those n's of 1 and 2 that you mentioned on your previous post... HOWEVER, just as you said, the issue is where the inequalities lie. if you're missing data where the groups are the most different, your ANCOVA is not going to catch it... or if you have a lot of data in one group and not a lot on another and those two groups are really not all that different from each other, you're almost guaranteed to find a statistically significant difference where there is none. it all comes down to paying a lot of attention to your data:

if you were to look at their variances, how different are they among groups?

what about running a missing value analysis? perhaps you dont have too much of a problem because you have mcar (missing completely at random) versus mar (missing at random) situation...(just for the record, we like mcar situations and we dont like mar situations)

anyways, as i keep on writting this stuff, i guess you can maybe just do your best with an ANCOVA and write up on your discussion section that a potential draw-back is unequal sample sizes. as a quantitative data analyst, i have a fascination with modeling data and doing the best (and usually most complicated, when required) analysis i can do so that the people who ask for my help in these situations are absolutely sure, beyond reasonable doubt, that their conclusions are substantiated by the analysis. i forget sometimes that not everyone is like that and, sometimes, reviewers dont know too much about stats beyond what they learnt at thei master's level. people i've worked with have had their manuscripts rejected on the basis that the analysis was "too complicated"(<--WTF!?)

anyways, my 2 cents for your post rite there.