I have owned a 356 Win Encore. Rimmed version of a 358. Killed one buck with it at app 135 yards. I had another in 7.62x54R (.308 Version). Also killed a nice buck with it at close to the same distance. Also had a 260 but never killed anything with it. It was capable of long range shots. I have shot impressive groups with it to 600 yards.

What I would do:
Send the Action off to Steve Stratton and have a trigger job done to it to start with.
For a barrel I would go with an MGM, BullBerry, or SSK. I have owned all three with no complaints with any of them.
I would strongly consider a .308 Winchester or 30-06. Lots of good bullets to pick from. Hits hard, and will reach out far enough to satisfy most handgun hunters.
Barrel Length? The last few I have ordered from MGM have been 15.875". Check hunting regulations for Maximum Barrel Length. I go long for more velocity.
Have a Four Gill Muzzle Brake installed, "and a good one". A highly recommend the Harrell's Precision 4 Port. I use the version with four holes in the top as sold and installed by Hunt's Long Range.
Forend: I have always went with Tony's in a 10" length, and a nice sand bag friendly profile. I prefer Charcoal Laminate to go with the factory rubber grip.
Forend Attachment: I have used the Bullberry Hanger Bar System on all of my Encore barrels to date. The first Encore Barrel I bought used from Mark Hampton was the Bullberry in 260 Remington with the Bullberry Hanger Bar System. I went with it on all my later barrels. Good accuracy off sand bags. HOWEVER the Bullberry Hanger Bar System is not a good choice if you plan to use a bipod. Recoil will break the Dovetail Inserts. If doing this over I would go with Two or Three Screws to attach the forend. I like Bipods a lot.
I would go with the Evolution Gun Works scope base. The flat one is just fine on most barrels. On my 223 barrel I ran out of UP Elevation at 500 yards. I switched it to a 20 MOA EGW Base. NOTE: EGW does make a 6 screw base. You need to contact them to verify who sells it. I believe Bellum, but I am not 100% sure about that.
SCOPE: This depends a lot on how you hunt. If you shoot from a stand using a rest such as sand bags or a bipod you can get by with some Rifle Scope's. I used the Weaver Classic Extreme 2.5-10X which is no longer available. On the 2.5-4X power settings you would think it was a Scout Scope. The higher the magnification the closer to the scope you will need to be. I have not had a reason to order one yet, but I would strongly consider the NEW Weaver Classic Series sold by Natchez. The lowest power available in a 30mm Tube is a 4-16x44mm. I am sure that this scope will "dial up" like the Classic Extreme. This scope is reasonably priced. If by chance you are not happy with it on the Encore, put it on a rifle.

If you hold the handgun at arms length, I would go with a Burris 2-7 Handgun Scope.

I do have a MatchDot on a 357 Maximum CVA Scout in a single shot handgun. I would keep the range down to not much over 100 yards with a Red Dot. I have taken several deer with a MatchDot mounted on my 9.5" 480 Super RedHawk. Works great at woods hunting distances.

Between my brother and I we also have Contender Barrels in 22LR, 223, 6.5x30JDJ, 35 Bullberry, 357 Maximum, 7-30, and 30-30AI. All are pretty much set up as above right down to the Stratton Trigger Job.

I have switched from the Encore to the Nosler M48 Handgun's. My 6.5CM was pretty much ready to go out of the box. I had Hunts Long Range install the Harrell's 4 Gill Muzzle Brake. My 22 Nosler was the M48 NCH version, and came with the Harrell's Brake installed, along with a Fluted Barrel. I really would prefer a 308 in the M48 Handgun, however Nosler does not seem to make them very often. I have not found one for sale in the last two years.

Just my 2 cents on the Encore Build.

Bob R