A lot of properties around coke handling are driven by the type of petcoke and its average particle size which determine the angle of repose. (I have answered various responses in archive blog on how high you can stack petcoke, the angle on conveyor belts & ect.).
The angle of repose for sponge cokes at +3/4 inch (0 X 6 inch) is 60 degrees, for shot cokes it is 35-40 degrees @ 16 mm (0 X 6 inch), and Fluid coke it is 20 degrees 60 mm (0 X 1 inch). When you stack petcoke on ground if you look at angle it forms to top of pile it would normally be 37 degrees for shot cokes. However solids are bad about grouping according to particle sizes (you can see this effect in can nuts when you shake mixed nuts the brazil nuts work to top & peanuts to bottom) – you notice the larger pieces work to the top & roll down edges and fines drift to bottom the more coke is worked or handled.
Most things around coke drum handling are designed around angle 20 degrees (bottom coke drum, conveyor belts, ect) and that is because of fines that separate out & sometimes come in slugs. So I think you would be best to design around that angle to minimize spillage and handling. Also shot & fluid coke are fairly hard at 45 to 28 HGI and they are going continue chew thru carbon steel like butter regardless of your angle – so your seven years is good run considering. (I once had really ticked off consumer who switched from coal to hard shot coke and it made his handling system look like swiss cheeze.)