1) British Eighth Army in the desert - that would be early production type M4A1 (very similar to the one K&C just produced) or M4A2 tanks. They would need features such as early (Grant-type) suspension bogies, British sand shields, 3-piece transmission cover, "direct vision" slots in the front, early gun mount (narrow gun shield without the "ears" beside the gun), British "Sunshade" brackets, Britsh stowage.
2) M4A1E4? That's a pretty rre bird - it is the designation for an M4A1 with 74mm gun that was rebuilt with a 76mm gun for Military Aid Program use. The "Kelly's Heroes" Sherman is an M4A3E4 - similar modifications.
3) The 4.5-inch ROcket Launcher T34, aka :the Calliope" was mounted on mid-production M4 (as seen in Normandy) or M4A3 75mm Wet Stowage tanks (according to photos anyway).
4) In the wide world of Shermans there are (as always) multiple possibilities. Some considerations are do you want wide possibilities for repaint or to do some unique tanks? For instance, a "calliope" rocket launcher was only used by the US Army in Europe in late 1944-and 1945. An M4A2 from the mid-production could be seen in the colors of the British forces in Italy or Europe, the USMC, the Russians or the Free French.
My suggestion would be a basic M4, probably a mid-production type. This is a "plain vanilla" Sherman but it offers options to be correctly painted for the US Army from Normandy onwards, and for the British in Europe. Correct color schemes include US Army in plain OD, US Army in black over OD, US Army in OD with white winter camouflage, US Army in black over OD covered by winter white camouflage, US Army in Italy in brown over OD, puls British in OD or black/OD camouflage both with various British or Canadian marklings. This basic M4 has NOT yet appeared in 1/30th scale and it offers some "growth" for other models. That same basic model could be remodelled as a ritish "Fireflay" tank with the 17-pounder gun. M4s also served as the basis for many of the tank dozers, for the T1E3 mine exploder. I know that HB is looking at more "customizing" optons for limited runs, so if the potential HB M4 was made with optional applique armor at the factory then they could use that hull to build an M32 tank recovery vehicle or an M4 gun tank from Sicily in the earth yellow over OD camo. An mid-production M4 as described could be fitted with the "calliope" rocket launcher. The model could also be offered with other options such as sandbag armor on the front, or a full rack of sandbags around the tank (K&C already did that with their "Strictly Limited" version. There are major options to customize stowage.
Another option is to use the M4 parts produce a run of M4s as built by the Detroit Tank Arsenal with a cast frontal upper hull. This is known to modelers as the "composite hull" and these tanks served the US Army in Europe and the Pacific and were another version that was supplied to the British who made a number of "Fireflies" from them.
Producing an early M4A1 for British desert use is a narrow range of appeal but it would cater to current demand for more dert armor. Once the parts are designed for the model it leaves HB open to using the bogies and some hull parts to create other early Shermans or using the parts on an M3 Lee or Grant projects, or an M7 "Priest". Building the basic M4 mid-production also provides a fund of parts for other Sherman versions for the future. As a model builder I'm always aqcuiring more Sherman parts for different models and conversions, so too could HB accumulate the more Sherman parts or experience from each model to allow creation of future projects.
Just a few ideas.
Gary Binder