Consider the following. At 400 ft (or lower) the PNF starts shutting down things. Unfortunately, he gets the wrong things shut down - despite the requirement for confirmation from the PF.
In over 20 yrs of instruction in sim and aircraft I have seen pilots rush into a procedure too soon and often get it wrong. In the debrief, he usually said "but I'd never do that in the aeroplane." To which the response always was "you've just done it".
All the various accel altitudes and SOP re where the recall items should be done are a compromise between getting the engine shut down, fire extinguished etc on the one hand and ensuring the a/c is flown accurately to a safe height above ground. Various airlines/manufacturers will adopt various altitudes/SOPs for these scenarios usually depending on their previous experience (or that of the Chief Pilot). Better follow your company's SOP in all cases unless they are clearly seen not to be adequate for the situation. After all they have been thought out in the cold light of day - not when you are at 200ft with an engine on fire.
For what it's worth, having seen hundreds (yes) of pilots rush into checklist items in the sim only to get them wrong. I'm firmly of the opinion that the best thing to do at very low level is DO NOTHING. PF flies the a/c and PNF monitors his flying. If you don't do that you'll burn the whole a/c not just the engine. It sounds obvious but most sim instructors will agree that one of the biggest problems is that of pilots rushing into drills and nobody is "minding the shop".
My personal view is that you should begin the drills for an engine fire or severe damage asap after 400 ft, WHILST ENSURING THE PF IS FLYING THE A/C ACCURATELY i.e it doesn't stop you from performing your prime role to monitor the other pilot's flying especially at low level and with a problem. Many airlines have changed the title PNF to PM - pilot monitoring - to emphasise this very fact. In any case, follow your company's SOPs and if you disagree with them make your objections known and perhaps they will think again if you have a strong enough case.
All other non-critical items should be held until the a/c has been cleaned up and it being flown to a safe altitude where both pilots can fully monitor what each is doing. Use the automatics to the max extent possible.