Certainly, by the rules of Chi, these words should be allowed. They are not plural nouns or inflections of verbs - they're adverbs I think.
Yes, MK, there are quite a few similar words, and most of them are not currently allowed. Many of them are so long that they're unlikely to have been possible in any puzzles anyway, which might explain why the question hasn't come up previously. There are a few words of this form that are already accepted, somehow: afterwards, earthwards and rightwards. Words currently not allowed are:
backwards
downwards
eastwards
forwards
frontwards
homewards
inwards
leftwards
northwards
onwards
outwards
rearwards
southwards
towards
upwards
westwards
I'll allow all of these.
I found I don't have to change hogwards. It turns out this does not mean "towards a hog" - nor is it a mispronunciation of Harry Potter's school. It's a word for people who look after hogs, so it is correctly treated as a plural.