I have a Mercruiser MAG 350 with Alpha drive. The engine block was replaced 5 years ago.
Was the new engine block from a Marine distribution warehouse/factory, etc.? or GM/automotive?
How was the new to you block listed; 'New or remanufactured, short or long block (meaning what new parts came with it such as heads, intake manifold, "new" to you front water circulating pump, etc.)...Have your receipt that may indicate new items?
The reason I'm asking is did your new engine happen right around the 2012 timeframe? If so then "maybe" you received a new to you water circulating pump of 2012 already mounted to your new engine which GM ended up having an design flaw to their circulating water pump blade impeller which caused different levels of overheating issues.
http://www.themalibucrew.com/index.php?/forums/topic/48335-indmar-water-pump-service-bulletin/
From PCM:
In the event you are diagnosing an overheat or running hot condition, the engine circulation pump should be tested and inspected prior to extensive diagnostics.
PCM is issuing Service Update SUP2012-03 to address a problem with 5.7 engines.
General Motors vendor for the circulation pump has supplied some pumps with impellers that do not meet the "hardness" spec on the metals. The impeller metals in some cases are too hard. This condition results in the impeller cracking and is no longer able to circulate water through the engine and exhaust system. The crack can be anything from a hair-line crack to completely broken as shown below.
^ If not then one other area you'll want to check would be the main water feed hose on the outside of the boats gimbal housing area (portside) for things like kinks, twists, cracks, etc., plus remove the stern drive and check for debris within the water flow passages as you may have something right at the hose opening when you first pull the drive off of the bell-housing....Sort of common....Ask Ted..
As for the T fitting mentioned if it's specific, yes there's one fitted/sized for an Alpha drive design where the impeller is inside the stern drive area and one for the bravo drive which uses an engine mounted, belt driven sea water pump impeller....See the "notes" under item number 20 if needed,
http://www.mercruiserparts.com/bam/subassembly/31747/7585/200