I know the frustration well. 12 years of it.
I'm sorry to hear it, having said that - I am a little confused- it is all too easy for a doctor to equate low residue with don't eat anything crunchy - so white bread, mashed potatose, rice all of which will destroy your blood sugar control especially if he is also still of the "fats are bad" school of thinking
The recommended daily intake of fibre for " normal" people is 25g. My average on LCHF for the last 6 months has been 13g - with no detrimental effect as far as I can see - in fact I have been deliberately trying to get my fibre up because it is naturally so low when net carbs are limited to 30g .
What is the actual limit of fibre your doctor has given you ? I have just put a sample menu from a low residue website into my cronometer and using the white parts of the recommended foods I get fibres of around 7g for 1500 calories - and horrendous blood sugar issues
Doing it the lchf way for 1500 calories - I can easily get to the same 7g for fibres - by switching out the carbs for fats - all still on the low residue diet list
I have just been through the list of ok foods for a low residue diet - and whilst it includes a bunch of things I wouldn't eat because of the blood glucose issues, it also pretty much includes the majority of my current LCHF diet. The way it is written presumes one is starting from a diet full of white bread and saying that is ok, but it doesn't say its compulsory to eat it.
Reading what you have written above, might fats be the answer instead of carbs. ?
The actual diet showing up as a low residue diet is in fact an LCHF diet just with a load of white carbs added and anything which has fibre attached pulped or strained - given the idea is that there is no residue and given that white carbs don't actually provide much nutrient either - if you don't eat them at all how can that be detrimental ?
http://www.webmd.com/ibd-crohns-disease/low-residue-diet-foods#3
would a combination of fish, shellfish, oils, fats, creams and eggs work for you instead? for example a shellfish soup made put through the blender with some added cream - - one of my " go to " dishes and almost zero fibre .
I'm sure you have already explored all of this so good luck in finding what works best for you.