Hi, Adam619, and welcome to the Grammar Exchange.
In this old thread, Betty Azar herself explains that both the non-progressive (simple) and progressive uses of intend are possible, similarly to what happens with the verbs plan and think.
Now, in this case in which the present perfect is used in the first part of the sentence to refer to an action (the washing of dishes) that has not taken place up to now, I don't think it would make much sense to use the progressive form because that would suggest that the process of making a decision is under way (it would be like saying: I haven't done it yet but right now I'm thinking of doing it). The use of the progressive would be more likely in a context in which the person is taking some time to reach a decision, for example:
- I'm intending to volunteer to wash up every day to make things easier for my wife at home.
I think in your example it would be more logical to use the simple form to mean that the person has already made the decision to wash the dishes and it's just a question of time before he/she gets down to doing it.