@copytype. I don't necessarily agree with their assessment. One question I'd be asking is even if the current engine is mounted in the proper position, is what model of engine? With the Evinrude 130, they have 4 models, 2 are 20" shaft, 2 are 25" shafts. Perhaps they have the engine in proper hole but the cavitation plate isn't aligned correctly with the bottom of the hull. The various mounting holes are there to align the engine properly and if you have a long vs extra long shaft on the OB, you need to adjust accordingly. To truly determine the proper length, you need to know the depth of your transom. If its 23" or deeper, you should have an extra long or 25" shaft (E130DCX or E130DPX) If its more shallow as indicated below the you'd need a 20" (E130DSL or E130DPL)
What is the extra HP going to accomplish? Getting you extra speed without trimming? I would suspect if I took your current engine, replaced the powerhead with a higher HP one, that trimming it to the same position would give you similar results. (You've suggested they want to increase it by 5 - 20 HP?) A 150 would be your max HP rating. I don't see why you'd need extra HP to prevent porpoising.
In fact, I have a 200HP on my 188, and if I get it to the right RPMs/Speed, I can make mine porpoise intentionally.
You mentioned SmartTabs. Are they installed on your boat? If so, you're the first person that's ever indicated this didn't correct that issue. (Just google it) I'd assume they've left them there since they've now drilled into your hull to install them. Perhaps they're not positioned correctly and need adjusting?
Not sure if this helps or not, but good luck and hopefully you get that boat back on the water where you and it belong.
Oh, and ignore the Short Shaft measurement in the picture as it really only applies to small outboards.