IHC,
You're asking an extremely open ended question here, and without pictures it's difficult to help.
But would it be possible to use a ladder for the insides? (If the floors are 'shiny' a Rojak ladder stopper or someone footing your ladder could be an option).
Being 'new to the trade' isn't really and excuse in the eyes of a customer for not being able to clean the insides effectively with a squeegie. You've got to take the time to learn the basic skills. WFP is just another tool, but using a squeegie must rank as the 'basic tool' you should know how to use.
You say the job is 'weekly', yet the customer is 'tight'. That normally doesn't go together. Tight commercial customers (in my experience) tend to go for the longer frequency cleans.
But weekly cleans are great, as they never really get dirty and you do them that often that you fly round them. So a low price for a weekly clean is not bad; especially if you can do it in all weather.
If it's a pain to do, give a generous quote, and if you don't get it; you've lost nothing.
There's nothing worse than taking on a big job at a cheap price; then just dumping the job because it's not financially viable.