I have a twin baby that I am working with who has a bubble palate.  They were born at 37 weeks, and were finger fed EBM, in the special care unit, as mom has plenty of BM.  Mom had severe PIH as was in the unit for over a week, but was able to pump her breasts.  Whe I first saw her, she had grade 2&3 nipple damage, and we used APNO for topical tx.  She did develop mastitis 2xs, but we worked through it, using probiotics and a yeast prevention protocol.
My treatment plan for the bubble palate was to use suck training using moms finger, and then we would do finger feeding, giving mom's nipple a break for healing.  The baby did very well and we were able to get her back on breast every other feeding, initially.  However, it became clear after many weeks of on and off soreness (she would slip and shallow latch, causing trauma)-we needed to investigate other options for feeding, as mom needed to nurse them both together, for sanity purposes.  This was an 8 week period of time.  We used a nipple shield for her and nursing became a happy time for everyone!  
The baby is now almost 5 months old and mom still uses a shield for her only.  The bubble palate is still present, and never changed.  Bubble palates can change, but hers did not.  We made sure she had a weekly weight check to be sure she was gaining.
When she was weaning off the APNO, we used Motherlove nipple cream, to protect her nipple integrity.  She is still using the ML cream.  I am not a big fan of lansinoh, as I tend to discover when using lansinoh, it can harbor yeast, especially when mom is taking antibiotics.

For your baby, I would use an SNS system, since moms supply is low.  I suspect moms nipple integrity may continue breaking down, especially if increased feedings are in order,  Have you considered using a breast pump, for stimulation and suck training/fingerfeeding for baby for nipple healing time  ?  What does the baby's suck organization feel like?  My baby had a strange posterior tongue humping and suck training really helped her, at least on my finger;)
Regards,
Jody

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