It sounds to me like the issue may be that you're crowding the pan.
Basically, to get everything nice and brown and crispy, you need enough space for all of the steam to escape. That picture you showed has potatoes stacked on top of each other -- that means as the bottom items cook, they're going to end up steaming the items above them.
At a diner, they have a large griddle to work with -- they can really spread things out. You're not typically that lucky in a regular kitchen, as you don't have as much space, and you have a lip on the pans that'll hold the steam in.
So, either work in smaller batches, or consider recipes that use an oven -- using sheet pans instead of a pan on the stove solves much of the problem.
One other trick is that most diners don't start from raw potatoes -- maybe with hash browns, but not for home fries, you're not going to get the nice soft interior in a reasonable amount of time unless you start with a potato that's already been baked or boiled. (If you're doing things in the oven, you might be able to, but not in a pan)
Just for reference ... I have a 14" cast iron skillet that I use for home fries ... and it's about the right size for cooking a single large potato, which might be two servings, maybe three for kids. (I tend to cook carb-heavy meals).
update : I probably should've stated this directly -- you want the chunks of potato to form a single layer in the pan, with space in between them.
This seems like a fun adventure. I'll say upfront that I've never tried what I'm about to suggest.
When I read your question title the first thing that came to mind is a Puerto Rican sandwich that is very popular in Chicago, the jibarito. It's a sandwich in which the bread has been replaced by flattened and fried plantains. I think doing something similar could yield nice results for a pie crust. You just press the peeled plantains between two cutting boards to get your desired thickness.
As far as not frying, you should also be aware that fried plantains are damn good. I've never eaten a plantain that wasn't fried. That said, if you are committed to not frying I have suggestions as well.
First, the boiling and mashing is right out. I don't think the processing you'll be doing will result in a crust that holds up at all.
Roasting, or better yet, pan frying in butter I think is the way to go. I suggest just greasing a large frying pan with butter and pan-frying the plantain over medium-low heat until done.
If pan-frying is not your thing either, I'd suggest just brushing them with melted butter and tossing in a 400 F (200 C) oven for 10-15 minutes (complete SWAG - never oven roasted plantain). With either the roasting or pan-frying method you may wish to sprinkle each buttered side with a little sugar to add a little sweetness and a nice carmelization.
Best Answer
Your clarification means a lot -- "baked" potato in the U.S. tends to be a whole potato cooked on its own, where the insides become fluffy and creamy, and is done with larger starchy white potatoes, or sweet potatoes work well, too.
Roasted potatoes, on the other hand, tends to be (in the U.S.) be smaller "new" potatoes, waxy potatoes, or even larger starchy potatoes cut up (eg, 'oven fries').
The starchy potatoes only really hold up well when roasting if it's very high heat or a short amount of time -- if you're going to be cooking them with the roast as there's going to be moisture in there, I'd go for a waxy potato (eg, Red Bliss).
As for the browning -- probably coat them well with oil, and if they're not brown enough for your liking when you pull the roast, as you're going to have to rest it anyway, drain the meat juices, crank the oven up to somewhere around 450F (230C) and leave the potatoes in for a few extra minutes.
ps. yes, I know a sweet potato isn't a potato. And I also tend to use Yukon Gold for just about everything, as it makes great baked potatoes, and roasted potatoes (although, not sure how well with a roast at the same time) and they're good in pot roast and stews if you don't add them too early.