What interesting questions!
There are a number of things to unpick.
My experience has been that IMAM (and CMAM) tend to be restricted to SAM treatment. Mostly I have seen separate or "semi-detached" MAM programming. I think there is an issue of incompatibility between SAM and MAM treatment protocols and with the support for these programs. I have seen programs in which inpatient care (TFP) was supported by the WHO with no co-location and integration with CMAM programming (e.g. no referral from TFC to OTP or back), OTP supported by UNICEF with no co-location with SFP, and SFP supported by WFP with no referral of non-responders to OTP or TFP. Integration between TFP and OTP does seem to be more common and better than between OTP and SFP. This is a difficult issue. Recent and ongoing work on unified SAM/MAM protocols may help.
I think we can be very bad at "horizontal" programming. Linkages between (e.g.) IYCF counselling programs and CMAM often do not exist even though both use community-based volunteers and are child nutrition programs. Getting MUAC screening into EPI programs and GMP programs can be difficult. Even the term "integration" is confused. In some places this can mean treatment in general health facilities (i.e. not in NGO centres or specialised nutrition units) with some NGO support rather than "joined-up" programming. This all sounds a bit desparate but there are examples of "joined up" programming that work. I think we need to identify and replicate this style of programming.
We are also not great at the numbers and costs issues. First the easy bit (using the data give above). For the 110 mm / 125 mm case in a population of 10,000:
SAM caseload = pnorm(110, 143.32, 12.94) * 10000 = 50
Overall caseload = pnorm(125, 143.32, 12.94) * 10000 = 784
MAM caseload = Overall caseload - SAM caseload = 734
For the 115 mm / 125 mm case in a population of 10,000:
SAM caseload = pnorm(115, 143.32, 12.94) * 10000 = 143
Overall caseload = pnorm(125, 143.32, 12.94) * 10000 = 784
MAM caseload = Overall caseload - SAM caseload = 641
We have no more cases. The case-mix has altered to more SAM and less MAM.
I think, however, your point is more about treating MAM at health facilities when the number of prevalent cases increases from 50 (or 143) to 734. That requires some thought. Costs can be kept down by reducing the size of the RUTF ration for MAM cases. Crowding can be controlled in a variety of ways by (e.g.) queue control methods. use of nurse-practitioners, and by reducing frequency of contact for MAM cases. Taking steps to increase coverage can increase patient numbers but can be cost-neutral down by finding and recruiting cases early so they can be treated quickly and the number of SAM cases treated in OTP or TFP reduces. This is an important point for the 110 - 114 mm group. If we can manage to get most SAM cases early (e.g. get a median admission MUAC of 112 mm or better) then treatment should be short and successful and costs reduce.
The reduction of the case-defining threshold to 120 mm is an option. It has been used in several settings. It may not have much effect on patient numbers in low/moderate coverage programs because most cases admitted will usually have MUACs below 120 mm.
Another issue with numbers is that we frequently ignore coverage. Average coverage of OTP programs is a little below 40%. We can assume that this will be lower for MAM (say 20%). This gives
SAM caseload = pnorm(115, 143.32, 12.94) * 10000 * 0.4 = 57
Overall caseload = pnorm(125, 143.32, 12.94) * 10000 * 0.2 = 157
MAM caseload = Overall caseload - SAM caseload = 100
This look more manageable.
BUT ... We have to be very wary about predicting caseloads from prevalence and coverage alone as it ignores incident cases. Estimating incidence from prevalence is a matter of ongoing research (UNICEF has an ongoing project) and it seems that we should inflate case-load predictions by between 2 and 17 times depending on location (the bigger numbers seem to be for West Africa).
The nutrition community is also, IMO, quite weak about costs. Much work in done on budgets and these are often large. Much less work is done on what is being bought for the money spent. I have looked at this in Nigeria CMAM programs. The supply side cost per life saved is about US$275. This cheap. The cost per DALY averted (using discounting and age-weighting) is below US$10. This is very cheap. I think we have to realise (and then keep proving it and telling people) that our programs represent exceptional value for money. They reamin cheap at 10 times the cost.
I hope this is of some use.