CJK: My local mason guru is no longer local. I'll have to rely on you as my unknown friends for schooling.
The rapid-set cement just had a hard look. Part of that involved minor destructive chipping and scratching. Now I have a hint of what "Inner10" meant: the stuff seems soft, breaking and cutting easily. The elements do not look like friends to its survival.
The front lip of the rapid-set has the most evident faults. The back of the pour shows one hairline crack that hasn't opened.
1. As to doing a new pour with the door in place, here is what I see;
* On the demolition.
There is open access from the back inside to the full height of the cement with the door in place. Here, I'm thinking that undermining the cement with drill holes in back and breaking the upper section sideways and down would be the safest method. From the front, grinding and breaking back underneath the threshold might be best. I think I can do this. CJK, if you want to call out surgical removal instructions, I'll follow them carefully.
*How I'd form a new material pour and finish it in the constrained area is perplexing while the question of what fills the measure of whatever open space your advise between the pour and the threshold remains open. If that can be resolved,
then this will add to the viability of this angle.
As an unrelated aside, you have previously said embedding aluminum in alkali-rich materials like cement or concrete is forbidden. I don't suppose the hardwood I think is cedar sandwiched in the bottom middle of the threshold might be fond of that either.
However, for any of you academically interested in this apart from the immediate topic at hand, here is a quick piece speaking to the other side of that issue, at least for aluminum:
http://www.concreteconstruction.net/concrete-articles/the-aluminum-and-concrete-controversy.aspx
2. With the door and jamb removed, a lot of the difficult goes away.
Framing the pour of a material you suggest (prompt set up would be wonderful) and executing it without interference would be much easier and the demo straightforward. If I very, very carefully mark the shim arrangement and door position before removal it might be possible for me to rehang it correctly particularly if the height of the pour is about dead even with the current level of the aluminum threshold. Or I can call my friend to do that part of the job he did well before.
3. Given how weak the rapid-set cement looks as a performer, an esthetic coating reminds me of the phrase lipstick on a pig.
The last goal I have here is to exasperate anyone and lose your kind attention. I'd really prefer to rectify the problem with the door in place if that is at all feasible. Anyone who can outline procedures there is invited. If consensus concludes removing the door is the only way, any detailing of pouring a new sill will be appreciated.
By the way, I culled a list of URLs that may be of interest to you for reading and reference in my prior masonry researches. If it would be any favor to cite them for your consideration, I'd be happy to do that.
You should be able to surgically remove that whole sill. Let the door hang in the breeze for a day. Form higher than finish and pour in properly mixed non shrink grout. Isn't there a mason there that can give you some guidance?