The extra information means we can do some some electrical
modelling on your system.
Its not clear if your watermaker
is belt driven off the engine or electrically driven using the output of the alternator. I have assumed the latter, but this makes a difference to your required battery bank size as if it is belt driven much more of the alternator output is available and a larger bank is needed to absorb this power.
I have made a few assumptions
1. Your 115A alternator will put out about 90A continuous ( this assumes reasonable engine revs)
2. 290w of solar will give you 100AHrs. This assumes reasonably good conditions
3. The watermaker
will consume about 45A
If we consider what would happen with various battery bank sizes
1. An infinitely large battery bank size:
So each day after solar you will need to make up 126AHrs from the engine alternator. During the 2 hour watermaker run you will be replacing 45A giving you 90AHrs. The remaining 36AHrs will be replaced at 90A, so will take just over 1/2 Hr.
So infinitely large battery bank you will require 2 1/2 hrs engine run time a day. You can go as many days as you want without an engine run, but every missed day will add 2 1/2 hrs run time. ( running the engine every second day would be 5 hour run time, every third day would be 7 1/2 hr run time etc)
2. Smallest possible batter bank (425Ahrs see below)
You don't want to run the batteries below 50%. 90% is likely to be your normal highest SOC. If you run the engine every day after the solar input your maximum deficit is likely to be 170AHrs on the worse solar days a minimum battery bank of 425 AHrs will be needed to keep the batteries above 50%.
A battery bank this small will probably just accept the 90A and 45A charge rate, so the engine run time will not change.
3. Compromise (850 AHrs)
If we size the battery bank so that the engine can be run every second if needed it allows use of the engine power during a long motor.
To go 1 day without running the engine requires a battery bank of 850Ahrs, but the run time is now 5 hours.
I think the analysis shows what many would have guessed without the maths, that a battery bank of about 850 AHrs is optimum. There is little point going larger unless you anticipate times when when you will be motoring for more than 5 hours. The 850AHr battery bank (or even larger) has very little impact on your engine run time compared to the smallest acceptable battery bank of 425 AHrs.
The biggest problem I can see is the long engine run time you will have 2 1/2 hrs is a long time to put up with the main engine and this assumes a reasonably high output that will require above idle engine speed. Unfortunatly a larger battery bank has no impact on this.
I think you may find this long engine run time frustrating and would look at ways to reduce this, which really involves more/better sources of power generation combined with energy saving measures and a larger (or an energy efficient) watermaker.