You should watch your rebbe's take on the matter posted above. There is no real solution to serve in a true Torah following way under a secular army with total different priorities but just a stated promise to "accommodate" or make it work. There will always be two different priorities and who has the last word. The current army chaplains or rabbanut rabbis are nodding their heads on what the generals tell them are matters of pikuch nefesh etc. Genuine independent poskim will never just take their word for it of course and it will lead to all sorts of problems and frictions. I think it's the other way around, in order not to upset the powers and public they're beating around the bush by coming up with "we do the Torah part" stuff. (Which of course those who aren't here to benefit from state or appease them have no need for all dishonest excuses.)
This.
The primary nafka minah is that the Charedi Rabbonim who send their constituents to serve - Mizrachim and similar - consider it important enough to compromise on this matter. Whereas, the Rabbonim that the Bnei Torah subscribe to (the ones that say "the biggest batlan shouldn't serve" for example) do not consider the matzav important enough to compromise on this.
Sigh... It would be absolutely lovely if there could be more tocho k'baro - more consistency in action - than there is. You can't say the army (the Chareid sections) is bad and then wander around Yafo because you are bored. But even when there isn't, it does not change the situation on the ground from the perspective of the gedolim.
As @yfr bachur said, a completely separate army run by poskim of their ilk (without doing more than taking advice from the generals, deciding on their own re: kashrus, Shabbos and shmiras enayim) is the only way it could work.
Lastly, no one can claim that they would know how a Gadol would think about any matter without explicitly asking them. Quoting the previous gedolim (regardless of shita) and applying them to today's situation is irresponsible. Let the current Gedolim do that.
First of all, I should just make clear that I used the word "talmid" in the context of that I went to his Motzei Shabbos shiurim for 5+ years and was pretty close with him in that context. He is not my primary rebbe (like
@mevinyavin has with RYBs), nor the Rebbe I go to for Hashkafa etc...
That being said...
We've gotten to the crux(es?) of the issue.
There are two separate charedi points of objection to serving. A. Yeshiva Bachurim, who toraso umnaso... should be exempt as their learning as they are bringing major zechusim that protect the entire nation. B. Those who are not TUM... can't possibly serve in the tomei shmad army that has no respect for torah/halacha.
What's the difference between the Chareidi points and the DL/Mizrachi/Chardal (meaning the frumest ones who respect learning) who don't have these issues? Ideology vis a vis how you view the state, the yishuv, Zionism etc.
The problem is that the mainstream charedi today is too scared (or embarrassed) to say this, as he is too chicken to risk getting the monetary faucet turned off. I'll have the monetary debate with
@Moshe Green in another thread (which we should start soon

), but the point is that they know that they are getting major funding from the Medina and don't want to give it up. I doubt they would agree to no funding for child daycare in return for exemptions.
So we are left to trot out platitudes about Torah Magna Umatzla, but not at the expense of my Bein Hazmanim (which BTW is just a cultural thing, You don't NEED 3+3+4 bein Hazmanim, you are just used to it and when it gets taken away you feel stolen from, but if the norm would be for shorter bein hazmanim, we would all get used to it and be just fine... as every american ben torah who started off in a full summer off yeshiva is once he gets to a Tisha Bav-RCH Elul yeshiva) in defence of the non service of burger flippers and street kids... which is mechalel the name of the true Maamidei Haolam... and causes the secular+ to believe that we are just making bad faith claims and demands (which in fact we may be....)