Hey CK, great to have you back!

You don't have to apologize, I know how these things can happen. I have been preoccupied myself the last few months. Don't worry you haven't slowed the scenario, because that has primarily been my fault!
So when I read your pursuit comment, I have to admit I get a funny visual of you on your knees begging your opponent "PLEASE don't chase me, I BEG OF YOU!"

Casualty reporting - As discussed above, there is a dialectic to be worked out between ASL, TO, and casualty reporting. But I think the "Lazarus roll" is a solid way of dealing with it, we just have to fine-tune the sliders, as it were. One point is with splitting casualties between units. I don't think dividing equally is too big a deal, most will not want to track individual unit casualties, and so long as we force equal division people won't be able to take all their casualties from crappy units, and none from the elites. One thing is I had not thought about how TO tracks crew casualties for Armoured units. I have lumped all the crew and infantry casualties together, but it is easy on my side to separate them.
Casualties in TO are tracked for each element. What that means is that an infantry company is tracked, plus any support platoons that are attached from the battalion level. E.g. the German Fallschirm Co has a MG platoon and a mortar section that were all attached battalion assets. Additionally it has a company of Stugs as part of the battle group. So losses are tracked for each of those elements (4 total). So dead crews matter (from the Stugs). When inputting back in TO, you can list the losses per element, if you have that information. Other times it may be cumbersome to do it that way... For instance if you were attacking with a full battalion of Fallschirm, OR you had a battlegroup of units cobbled from 2 different Fallschirm battalions, you could just split casualties as proportionally as possible rather than try to keep close track. I think it will be fairly easy to track different unit types with the Americans being a good example in this scenario. They have an infantry battalion attacking with an engineer co and tank co attached. It is fairly easy to tell which casualties belong to each of those units. Big picture, it is my current estimation that in most cases it is going to be reasonably easy to differentiate where casualties were taken. If it comes down to it I think it would be perfectly acceptable to SWAG it (Scientific Wild-Ass Guess). I don't want to force players in to taking copious notes...unless they want to. Does this answer your question CK? Am I making sense to everyone, or am I talking in circles? This is good CK, you hit on an area (varying options of inputting battle losses) where I have not thoroughly fleshed out all the details.
Persistence and casualties - Much discussion above, so I won't repeat it here. I think that we will have to adopt some sort of normalization in terms of both casualties and advance to end up with meaningful battles that don't end too quickly, as this one did. But the more we normalize, the less effect that playing the engagement out has, so why play the engagement, etc... This is the biggest issue we have right now, and I think we are going to have to work out different options in terms of selecting a "normalization level" and let players choose.
I just want to reiterate that there will be a significant range of casualty "allowance", but once it reaches a certain point then players may want to normalize results to some degree (or not based on player preference at taking everything at face value regardless of outcome). In your latest battle, we may end up taking everything at face value and moving on. As for "why play the engagement" in terms of normalization I would respond "because they want to". If you go through the trouble of setting up a battle and things go badly very fast, then why not play it out more for fun? OR like Cat did, they reached a conclusion for TO after substantial play time, then continued to play it out strictly for fun. OTOH, if a battle ends prematurely the attacking player may well want to say"note to self: don't do that again!"

, and then move on to the next engagement. I don't think we need to completely confine ourselves, and we can make it work to suit our preferences...and our preferences may change from battle to battle. In my humble opinion, the key will be mutual agreement between players on how to handle results before a particular battle commences.
Artillery - Much of the discussion above related to how to incorporate artillery without making it totally unbalancing. So I tried a mechanic to reduce the amount of OBA on the board. Even so, the arty was overpowering for the defenders, although it must be admitted that my opponent was quite lucky, and I quite stupid to give him a target. But still, artillery is VERY powerful in ASL, and the number of modules on board is, although historically consistent, currently far too high. It is kind of a rule of thumb in ASL campaign games that no more than 2 OBA modules may be used per side per day, and I am thinking about adopting this. But then how do we align this with the high amounts available in this TO operation, especially to the Americans? I am open to suggestions here, frankly, but am currently thinking that for each TO battery available for support, a roll will be made to see if it translates into the battle, with bonuses for lighter calibres, which must roll first. Once 2 modules are "received", then that's all the side gets. Another way to do it is to allow all the modules, but vastly change the ASL chit system for battery access to make actually getting a fire mission quite a bit less likely. I am loath to do this, however, as it involves changing core ASL rules.
Artillery...yes this is an important aspect to discuss. As you mention, there is a careful balance. One thought for ASL would be to allow the arty limits you discussed, and then if you possess artillery in excess of this you could consider a few different options like: 1. increase your force size proportionally (i.e. trading artillery power for more on-field units); 2. Decrease the amount of enemy forces based on artillery proportions. These are just some quick ideas to get the juices flowing.

This brings up a question: Canadian Cat, how did artillery work out in your battle using CM? My impression is that it went fairly well in that there were plenty of assets to use, but it did not totally dominate the battle. Is that a fair assessment?