Hmm, you say it executes first in page 4000-7FFF and then in 8000-BFFF? I will check this, and if so, that can be issue, hence compiled with ORG 4000h, so it can do absolute calls and jumps from window 8000h to window 4000h, where can be unexpected slot activated. Otherwise should not be an issue, hence I check SLTWRK record for nonzero if there is already allocated memory and exit initialization prematurely expelling allocation repetition. So I can check not only SLTWRK for window 4000h, but also 8000h and maybe 0000h and C000h.
A real interface on a real system NEVER, EVER should do that unless designed to do so. Mirroring is a side-effect of not having the proper connections to selection signals for your type/size of ROM. On emulators, that is a different animal, ROM files do not have a reader information indicating what kind of mapper that ROM file uses and in the regular ROM files, that do not need mapping, if there is mirroring or not. Some game cartridges count on mirroring to find out if it is a copy or just because it is useful to the game to have a copy mirrored on another page, so, by default I think that all, if not most MSX emulators will mirror 16KB rom files unless you explicitly tell it is a 16KB rom. You can make your life easier by just adding the H check on your ROM entry point, if you do so, it will only execute when @0x4000 (or 0x8000 if that is your thing).
Thanks for the sources, I see you are doing interesting thing, I will examine for new ideas — my project is much more humble. But I am still not sure that problem is in dual initialization — I'd saw multiple records in SLTWRK while debugging. Problem is disk bios memory allocation function corrupts some machinery, even I do not write to allocated area.
UPD: pretty same I did, but I ignored subslot, so better I'll add this for a case. And I see your malloc routine pretty differs from what I used — it rather simplier, just moving HIMEM down and nothing more. Is it ok you at least do not move stack? I'll check if your routine is better for my case.
What compiler do you use? I am on GENS80, it limits me to use 6 character labels. I suggest you compile on PC.
My project also started very humble, by looking at great examples out there and researching MRC and other sources, got to improve it to this point, so the general idea is that, start small, and grow on it, starting with huge projects might end up as a bad thing as you may quite because it would take quite a while to get something working. I always like to break into small tasks and get things working slowly, one by one, this way I feel motivated every time a small piece is working.
Not sure about open msx as I use BlueMSX as it was quite easier to integrate a few extra hardware emulation to it than it would be to add to OpenMSX, but I'm pretty sure someone already asked this question around here, if you don't find through search, try asking Manoel, he is a great guy that has great knowledge on OpenMSX.
About moving HIMEM, it works fine, on my experience, as long as you do it after all adapters are initialized. It survived going to basic, executing something, and going back to DOS... 
Since what I did has no use if you don't have DOS, don't need to care if no disk rom is available. Notice that in my case I didn't want to use H_STKE to do the memory allocation as I've found out that ESE SCSI doesn't like when someone hook to H_STKE before it, but pretty sure it should work fine on H_STKE otherwise.
The DOS2 memory initialization routine is fine as well, but you need to adapt it to work for you, as there are some memory initializations and shuffling around that you shouldn't do, unfortunately can't help much on that as I really don't remember what need to change on that routine for something that is not a disk adapter, but by debugging and understanding the calls and addresses and pointers it is moving, you should be able to figure it out after some thinkering.
I use two Assemblers, one is SDASZ80 which I really recommend you never try unless you want to create libraries for SDCC... It is non-standard, crazy and I really don't like it, but it is what you need to use to make sdcc libraries so I've used it for the MSX2ANSI library. For all other projects I like to use sjasm 0.42c , but there are lots of great assemblers, I've also used glass and like it a lot. And yes, nowadays everything MSX related I do is cross compiled, so I edit the files and compile on a PC and for quite a few projects also debug on o the PC using BlueMSX or OpenMSX as well. 
Hook H.STKE
Just tried with the hook. This does not work. Even if the only thing I do in my H.STKE is restoring old hook and JP to it, the system continuously reboots. After I remove installing my hook, the system boots well. Surprizingly, there were no hook to backup, 5×0xC9 were backed up, but nevertheless. Are you sure right hook it is?
About moving HIMEM, it works fine, on my experience, as long as you do it after all adapters are initialized. It survived going to basic, executing something, and going back to DOS... 
Since what I did has no use if you don't have DOS, don't need to care if no disk rom is available. Notice that in my case I didn't want to use H_STKE to do the memory allocation as I've found out that ESE SCSI doesn't like when someone hook to H_STKE before it, but pretty sure it should work fine on H_STKE otherwise.
I think I am doing something wrong and it is time to share some code.
init
in a, (0A8h)
rrca
rrca
and 003h ;Bits for 4000h-7FFFh window chosen slot.
di
;Code skipped there to set some RST30-based hooks
ei
push af
call getwrk ;HL is our address in SLTWRK
dec hl
dec hl
ld (hl), 1 ;Set flag that old H_STKE stored here
inc hl
ex de, hl
; Check if RST 30/DB slotid/DW init2/RET are already there (these comparisons are obviously not optimized, but let make it work first)
ld hl, H_STKE+4
ld a, 0C9h
xor (hl)
ld c, a
dec hl
ld a, init2 / 256
xor (hl)
or c
ld c, a
dec hl
ld a, init2 & 255
xor (hl)
or c
ld c, a
dec hl
pop af
ld b, a
xor (hl)
or c
ld c, a
dec hl
ld a, 0F7h ;RST 30
xor (hl)
or c
ret z ;Stop initialization hence H_STKE is already replaced (this is because init is called twice)
push bc
ld bc, 5 ;Backing up H_STKE
ldir
dec hl ;Our hook for H_STKE to point to init2, not optimized too, maybe LDIR later.
ld (hl), 0C9h
dec hl
ld (hl), init2 / 256
dec hl
ld (hl), init2 & 255
dec hl
pop af
ld (hl), a
dec hl
ld (hl), 0F7h ;RST 30
ret
And init2 is as simple as
init2 call getwrk dec hl ld de, H_STKE ; Restore old H_STKE ld bc, 5 ldir ret
I checked it in the debugger, and while H.STKE is 5×RET, it was called multiple times, that made me think it might be wrong hook, but the description in the hooks docs pretty matches your advice, so, more likely I have a bug in my code, and it is probably ok to be called multiple times. It is also called once for my routine, which restored well to 5×RET, and system reboots after that.
