So like yeagerville area? Plenty in range at any rate. Monroes multicast range runs all the way into Sylvania so not an issue for you at all.
And yes, when listening to one of the feeds there is a delay. It can be kind of disorienting at times. Also keep in mind if you are listening to a feed they may get some stuff you don't, miss some stuff you pick up. It varies by scanner, location, number of channels you scan and just shear luck and timing. It is not uncommon for someone to have to scanners of the same model with the same programming and have one miss calls the other picks up. Scanning is kind of a random act by nature. And the more channels you scan the larger the odds get of you hitting that one channel at the exact right time. This is why people that are serious about scanning, or stream own multiple scanners. You hear a lot more with multiple scanners scanning specific areas or frequencies than you with one trying to scan them all. Unfortunately for some of us, owning one 3 or 4 hundred dollar scanner is either all you can afford or hard to justify. Let alone a whole freakin bank of them with antennas and hardware to connect them all. I have seen some these guys set ups and estimate the rough cost based on my shopping around for one. Some of them have enough invested that you could buy a snowmobile, atv, motorcycle, hot tub, a couple nice hunting rifles or a nice used car. It all depends on what you want more I guess. Or justifying it with your other half if you are married. Or build up your collection over a period of several years maybe, which is what I would guess most do.
I basically do what you are wanting to do at times. I own a 325p2 though, so no built in database. Instead I have a separate database I can upload if I am going to go for a drive out of town. It has Lenawee, Monroe, Wayne, Washtenaw, Lucal, Fulton and Henry counties programmed in. Each on its own system with a quick key assigned. It is very easy for me to just reach over and hit a button to toggle them on and off as I drive through different areas. There is about 1100 channels in that database and it only uses about 3 percent of my scanners memory. Not sure how that would work on a 436 since I don't own one, but the dynamic memory system must be fairly similar I would think.
Most of lenawee police and fire is still analog, so you could pick that up from your house if you had a good antenna. Heck you might get it with the stock one. You won't get Tecumseh or Adrian police though, they are not very strong. You would probably need an outside antenna for those. But the sheriff has a pretty strong signal. I can pick it up with my stock antenna all the way out to central ave on highway 23 in ohio. They do have one channel in the trunked system, the lenawee 911 dispatch is both analog and trunked. It sounds like crap on the digital system though. The analog channels are much more sharp and clear.
From what I understand the 436 has a favorites section in it. So it might be an idea to use the software to program exactly what you want to listen to into some favorite sections. Don't ask me how though, I don't have that scanner so I have no clue exactly how that works. I am sure there some videos on how to do it though.