Recommendations for Non-Aeros?

The Frogs are considered "cross-over" blends and may be a good place to start your Latakia journey.
Have you tried any OTC's like Prince Albert?

That would be a good intro to a mellow Burley that is slightly sweet.
The PS Luxury Bulls-Eye Flakes have a sweet Cavendish center and might be a good VaPer to try.
For a straight Virginia that is sweet, try Mac Baren Va #1.
Hope that helps a little!
Edit: PM Sent

I like Frog Morton's Cellar. It's the only one in the series that I've had so far. Try some Orlik Golden Sliced too. They are both yummy. I've lost interest in Aromatics since I discovered EMP and OGS. And yes it is easier in the tongue. Just don't smoke too fast.

Funny thing. I started with non aros, and I learned to smoke with them. Lately I've tried some aromatics that were professionally hand blended, and I find I enjoy them too!..not only that, but, I've tried some lat blends and they're fine smokes.

It's really not so much the tobacco that causes burn. It's your process. How you could go on burning your tongue for a year without finding a remedy is a tribute to your, um, perseverance.

Hearth and Home Anniversary Kake is my vote.
I also think you need to review your technique a bit too see if you can eliminate your tongue bite.

I'm not certain that aro's cause tongue bite and that non-aro's will automatically be any better for you.
But, if you want to try a few different blends, I'll second PS Luxury Bullseye Flake and recommend Frog Morton (on the Town is my favorite, but I could not say whether one Frog is more prone to bite than another) and 4Noggins Bald Headed Teacher. BHT has just a hint of latakia and some sweetness and nuttiness and is very easy to smoke.
I hate to say that Frog and BHT are "cross-over" blends because it makes them sound like they have training wheels and that you only smoke them until you move on to "real" blends. These are excellent blends in their own right. I have a lot of things open and in rotation (many "English," some VaPer, and a few aro's) and always have these on hand and enjoy them frequently. But, they are easy to smoke and not overwhelming, so a very good choice for someone looking to try something that is non-aro.

I hate to say that Frog and BHT are "cross-over" blends because it makes them sound like they have training wheels

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From 4Noggins Website:
A perfect cross-over blend for those looking to begin enjoying Latakia. The Latakia is married with an aromatic flavoring to arrive at a pleasant mix of smokey and sweet. Providing very little bite, this is a good all-day smoke.

For crossover blends from Aros, I suggest:
Rattray's Marlin Flake - sweet, stewed fruit and among the best VaPers of the non-spicey variety
GL Pease Barbary Coast - nicely brandy-flavored Burley with Virginia and a dash of Perique
Erinmore Flake - for a fruity VaBur flake
Pipeworks & Wilke No.5, Bestmake, and Pipemaker's Choice - for the Queen of aromatic crossover English blends
Orlik Golden Sliced - Sweet, smooth Virginia flake
Stokkebye Luxury Navy Flake - Sweet, smooth VaPer flake
Stokkebye Luxury Bullseye Flake - A bit more Perique with a smooth Cavendish core to round it out
Two Friends English Chocolate - like the name says...

Cobguy -- I stand corrected and will not hesitate to refer to BHT as a cross-over blend in the future.

Dunhill's My Mixture 965 is a good non-aromatic that pleases many. Another really fine

mild English is Nat Sherman's 536, with Latakia but in a pleasingly supporting role. Another

pleasant non-aro English blend is Sutliff's Westminster, or G.L. Pease Westminster, both

tasty, gentle non-aromatic blends. Also Altadis Fox and Hound. One or more of these

ought to please you.

I sip 3 of the Frogs - Cellar, On the Bayou, and Across the Pond. Like Orlik's Golden Slices too. Like Patrick I'll have to take that Frog to Town one evening. To me all the Frogs are great all day smokes and I love Cellar after a meal. Have just started back after a long layoff and am looking for more non-aro suggestions also.
Toadshade the Frog Sipper

I bought tins of Lane's "Crown Achievement," and LEO, as a new pipe smoker. I started out with Captain Black white label and Villiger's 1888 Mid-Day, but I've discovered a real fondness for the spiciness of the Lane's and the LEO. My best advice is to just jump in. You may not like the first or second bowl, right away, but it grows on you and you'll find yourself reaching for it; especially once you get tired of all of the sweetness of the aromatics and milder tobaccos. Just my humble opinion...