Mast rake theory help please

I understand what you're saying and that that will achieve the correct rake and forestay length. If I then release the backstay and tension the rest of the rig won't this still result in a loose forestay at rest?
I'm beginning to think the backstay is just too long for some reason and needs a method adjusting the length during set up.
I'm away from the boat now so can't test.
Yes, on sportier boats it's quite normal to let the backstay off and have a loose forestay - but it won't be sagging like it is now because you'll have attended to the slack shrouds.

If you're not getting sufficient backstay tension - and especially now that you've ignored the tuning guide and reduced the rake - then I need to know why you're questioning the backstay length. You haven't said that you've run out of adjustment on it, but now would be a good time... If you have, then as we've said several times, it's either been put together wrong or the rigging has been made too long. If you haven't run out, then how are you defining 'enough' tension?

The problem here is that I still don't think you've given the whole story. It's a new-ish to you boat. What was the rig like when you bought it? Was it on the boat? Was it nice and tight?
 
I'm wondering if 'the manual' is mixing advice for fractional and masthead rigs?
Masthead rigs are IMHO 'orrible things with the one saving grace that the backstay directly opposes the forestay, and the shrouds don't have to be used to tension the forestay.

I think we are beyond the limit of what can be done over the interweb TBH, I suspect people are at cross purposes.

Always bear in mind the boat may have undergone mods since new and the manual may no longer apply?
 
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