I just replaced our Sharp R-1820 Micro/conv oven in our '05 HR. I ordered the Sharp R-1875(Home Depot), which is an upgraded/newer model of the 1820...same backing plate and all the mounding bolts are exactly the same.
In addition to the two angled bolts from the under side of the unit that attaches near the top of the back mounting plate, there are two additional mounting bolts at the top, toward the front and along each side of the oven. If you buy the updated version of your oven, the R-1874/1875 comes with a backing plate template and a top mounting template. I used our old oven backing plate because the seals were in great shape, so I'm saving the new plate...just in case??
About those two top mounting bolts...Our top mounting bolts were hidden by a false bottom in the cabinet. I took the new oven's top template and marked out where the bolts should be and hole sawed two 1&1/2 inch holes in the false bottom...wa la, top mounting bolts exposed.
The back of the oven sits on a lip of the rear mounting plate, so I removed the angle bolts first and the DW just held the front of the oven(very easily done...no strain) while I took the last top bolt out. BTW, I took the box that the new oven came in(do not tear this box up, because it is marked to make cut outs that make the removal and installation VERY easy without too much lifting effort by the installer) and put it under the oven on top of our cooktop. Then once that last top bolt comes out, it's just a matter of tilting the front of the oven down and letting the oven rest in the cut outs in the box. Also it helps if the other person feeds the oven cord through it's hole in the cabinet.
Our old oven had the 59 second shut off syndrome so I wasn't too excited about spending a gob of money on a 9 year old oven...I just went ahead and replaced it. We really liked the old oven, when it worked.
One other thing about the installation...one of the angled bolts, at the top rear of the oven, came out of it's metal 'tang'. I didn't notice it and had to take it down to reinstall the bolt back into that tang(bolt would not line up with the encapsulated nut in the backing plate. Practice makes...
Anyway, if you go with the updated version of your oven, it's a pretty easy install...although this sucker is on the heavy side and is a little bulky.
Hope this helps a little...good luck with it.