aotz style spawns -
I think this can work, but in late game there is already some pathing/crowding issues. Maybe, when a spawn is bought, it replaces some existing spawn in the wave. e.g. you buy tanks/bruisers it replaces grunts/footmen, siege replaces catapults, etc.
construction options -
Shipyards are useless and will die immediately when a lane pushes and other than infernals and the rare chimera/frost wyrm backdoor the construction options for either side are nearly worthless especially for their cost.
Other than non-optimal team situations, the biggest thing about this map that really stands out to me is how ending the game is only possible after a large period of time passes and the enemy team allows you to make repeated attempts at the queen/king of austria.
When I thought about this I momentarily considered several points...
1 - The flags serve no purpose at level 21. By then you are usually full build or close to it (unless you get very lucky RNG on runes but runes are opt-in.
What could be done about that?
* You suggested AB-styled respawns. This doesn't really solve the issue of the king being a fortress with the right heroes behind him, or that the gyrocopter has a huge siege advantage (you said it was getting reworked but I'll touch that in a moment so hold this rod)
* Attacking minion spawns. To me this would have to very carefully be designed to avoid a moba thing since that is what you are probably trying to avoid. But if a team has a lasting commanding presence on the map it could help put more value in the objectives once they otherwise have nearly no use other than vision.
* Environmental advantage/disadvantage - Maybe a longer term thing. Currently, advantages are mostly accrued around the first ten minutes in the game by the first fights snowballing a gold/level advantage off of early caps. But since you can't actually hope to kill the king or really do anything, this advantage doesn't really peter into anything meaningful. Maybe being able to build stuff around flags (with gold or something) or having particular effects in the areas around the flags will give them a bit of value. Think the water around blacksmith in AB.
2 - Items.
So you said you didn't really like how the item system currently was working out. I think the big issue is the one shop is specific recipes and the second shop is a bunch of hidden recipes that share combo items with the first shop (every time I try to make the MS gloves I invariably end up with some other combo item because of the order I did this in).
In LoL I planned to make a specific item require reagents from neutral minions (or bought with exceptional gold) to combine with that item, possibly at a specific location (helm's deep for example).
If you decide to associate respawn points with flags this is going to fuck with item balance a lot (those stones will become even stronger because you will be able to make more use of them before the mid/late gold starts to outscale in terms of cost-reward).
You mentioned something about dual stat distribution always being dumped in favor of sole stat distribution and maybe some auto attack benefit passives might help. Something like a bleeding dot or something that stacks with AA would help some heroes like warrier man x stay relevant against the very high CC on the loladin side. Or things like a mana shield item.
There is not a lot of incentive in building defensive because of high damage/utility abilities and the safety net of the long distances and comparatively short respawn timers. Late game only a few select heroes pose serious king siege threat and even then you are likely to die to sheep with the exception of the gryocopter. Which brings me to 3.
3 - siege heroes.
The Gyrcopter currently is capable of killing the king without ever really needing to put itself in danger. The caveat of this is that it takes quite a long time and other players can stop it.
While I consider the missiles in themselves pretty toxic since they do a ton of damage and are unavoidable in most cases (not to mention the safety), I don't necessarily consider the role that this playstyle imposes bad in itself. Indeed, I sort of imaged my hydra as a psuedo siege-capable hero with fair range and some summons and aoe built into it for this sort of purpose. Right now the map is mostly about 1v2's, 2v3's and rarely team fights for aforementioned reasons. As it is, siege really can only show itself in a form like the gyrocopter because anything close to the king will get reamed by respawning players and really can't hope for much support besides warrier man x's recall which is only one person.
Making long-range weapons have some counterplay, like arcing projectiles you can avoid or missiles you can destroy (my preferred approach in apex) opens up the possibly to reach out and touch stuff like the king or his defenders without needing to die for that 200 hp of damage on him. But also both teams having access to these kinds of tools opens up options. Previously the Nerubian served this role because he could safely attack the king/the teleport point which effectively served the same purpose but without the range.
Warning: dialogue contains politically incorrect content. Viewer rearsore may occur.