Just lower your power needs by going LED lights in headlamp and tail, an original working alternator with a well magnetised rotor will have no issues even with the added drain of the starter motor over the previous models you can run lights on all day. Check your rotor by removing it and then placing on the floor, place a large screw driver on the top magnet and lift, get it replaced or remagnetised (A O Services) if it stays on the floor. 

You would have to ask AN why they can't supply a 180W single phase.

If your current setup is working then leave alone, if its not then you can get 200W single phase combined regulator/rectifiers to replace both rectifier and zeners. Being a MK3 wiring changes will be needed as the paired zeners is a unique setup as they are used as diodes as well as voltage regulation, you would need to replicate the pre MK3 setup.

That is special one to stop Trispark ignitions from being interfered with by other rectifier/regulators output. Unless you have Tri spark ignition (which is very sensitive) then you do not need to pay out the extra expense. A cheap Honda type will suffice as long as it can handle 200W or 17A but lay off the Wassell one as that suffers from leakage to earth which drains batteries. I use a Mosfet rated 35A for my 3 phase alternator.

The old setup is electronic too, it was dynamo's that had mechanical regulators.

I used a Tri Spark ignition with Podtronic rectifier for a long time without issue in my MK3, the problem tends to be the pre MK3 which have the smaller battery. Noticeably, those with Alton starter and Tri Spark ignition didn't experience problems either, and this is quite an old combination of equipment. 

The Tri Spark ignition and Mosfet rectifier are quality items, simple to install. However the WLA will not work with the rectifier, but again upgrade to Al Os battery status monitor, brilliant bit of kit, on a couple of occasions it has indicated all was not well, and the faults took some finding.

The old idea of tapping off some of the AC to make a warning light function is old hat. It indicated the rotor was going around and the stator is outputting AC at some level. It now makes sense to use all the output from the stator to be rectified as efficiently as possible, and with LED tail board of lamps and compact H4 led which does not get hot and fits the MK3 headlamp shell, you'll only need the RM 23 stator. The latest 3 phase offerings of stator don't fit inside the chain case, so if you go that route you'll need to find an older version of 3 phase stator. 

I have recently completed a Mk3 rebuild using a RM23 and Trispark Mosfet, as Ashley states [and Trispark did not] the standard warning light assimulator is not compatable with this type of setup it took me 3 WLA's to find that out, another update is a bigger battery in my case a YTX16 [I believe a YTX20CHBS is the same dimensions] and as stated the YTX16 fits with the standard MK3 airbox.

The single phase alternator stator on the MK3 is an RM23 (two wire)

Lucas part number is: LU47239

You can also find it under Wassell part number: WW10190

It is a 16 amp stator (compared to the 10 amp RM21 on the pre-MK3)

The zener diode used to regulate the output at the time was right at it’s limit on the pre-MK3, so when the higher powered stator came along, Lucas had to re-visit the whole idea. Hence two zeners (used on the AC side)

It’s a compromise for sure, and the charge voltage to the battery is around 0.7 volts down compared to the older charging system.

The three phase system is an excellent upgrade, as you can achieve a similar charging output at lower RPMs, so much better suited to riding in today’s modern traffic.

I have written a lot on my site about charging, and the importance of balancing your power consumption with your charging.

Some information here: https://granttiller.com/choosing-a-new-alternator

Don’t hesitate to reach out if you have any questions.

I have had good success with the “Standard Charge Warning Light - £16.95” from Improving Classic Motorcycles.

I like them, as they allow you to retain the original warning lamp, which is particularly important with the MK3 and the quirky little instrument panel.

https://www.improvingclassicmotorcycles.com/products.htm

A couple of notes:

• The Tri-Spark MOSFET reg/rec is not a special one to stop Trispark ignitions from being interfered with.
  It is a more modern type that provides a smoother power output versus the older reg/recs.
  Tri-Spark electronic ignition issues were only reported to manifest on specific models of PODtronics reg/rec.
  As the OP has a Lucas Rita, this is of no significance.
   
• The two zeners on the MK3 are not matched at all.
   
• The charging technology on all Commandos is silicon-based, and very solid state (ie nothing is mechanical).
  So unless you go up the MOSFET route, you are not actually updating anything to more modern technology.