I, however have a different idea, consisting of pretty much two parts. The first would indeed be a range increase, though not as extreme as most are proposing -- something along the lines of a 60 - 80% range increase for short and mid ranged weapons systems, and a ~50% increase to long range weaponry.
While the numbers may or may not work, I think we all agree on this.
The second would be the ability for starbases and all other facilities (excluding, naturally, the Vasari Orkulus) to move in an orbital path around the world to which they're attached. This would render circumventing defenses a far more difficult task.
This would really screw up our ability to protect our structures, and would be completely unworkable for things like phase inhibitors which need to be placed precisely in order to have the desired effect. They are generally defended as well, so we can't have our defenses moving all over the place.
Finally, Starbases are either vulnerable to the point of uselessness or completely bypassable while defending an unihabitable node. Given the early information available, this does not seem to have been intended. My suggestion for this problem is quite simple; over an inhabitable node, Starbases have options available to help increase the resilience and prevent colonization of said node (or are at least supposed to - they currently seem to be bugged.) For a Starbase in an uninhabitable node, I suggest that this ability, which in such a place is useless anyway, be replaced by researched option that would allow the base to acquire a constructor and a number of tactical slots, which would allow for the creation of adequate defenses, locking the route down with phase inhibitors, etc.
This seems like a decent idea to me. I think starbases definitely need some sort of additional option to help defend uninhabited nodes, but I don't know if creating structures would be the right answer. I'd rather just see additional options for the base itself, such as additional hangars and some sort of phase inhibitor functionality. These probably wouldn't be used for SBs in planetary grav wells, as using those slots would be wasteful when the planet can already provide those structures. I think there's a growing consensus that more hangars is a necessary option for SBs anyway. The phase inhibitor function may even help solve part of the issue of SBs being too easy to bypass.
A better option for most mine deployment systems would be to borrow the previously suggested "fields" idea and place them just as you would an orbital facility. Click the planter, click the "place mines," click the location. If the planter is a ship, you should be able to set its usual "default position" which it returns to between refreshing fields. That doesn't necessarily mean that mine fields should disapear after X time (in fact, I'm utterly against that; the fact that fields hang around long after their creators are gone is important in many battlefields), but detonation should deplete the field and require it to be refreshed by a layer whether that be a Hangar facility or a mobile ship. You should definitely be able to destroy your own mine fields by scrapping them, pointedly.
This is basically how TEC mines work now. I think it's fine, except that a cap is needed, as well as the ability to scuttle a group of mines all at once. We also need to have a better method of laying them to form barriers rather than just amorphous blobs of mines. I can't really speak to the Vasari or Advent issues yet.
For defense, it seems obvious to me that while Scouts should / can detect mines, Defense ships of all stripes should be able to detect and destroy them as well. In fact, I'd give the edge in detection to Scouts and in destroying them to Defense; a dedicated mine-clearing fleet of a couple of Scouts and a handfull of Defenses would be an ideal pair-up, and certainly something to hold in reserve for when you need them. Scout ranges on mine detection really need to be much, much wider; probably more like a third of an average well. Engagement ranges should be much lower, of course, but that's sensible. SC might be able to clear mines (possibly with an upgrade for everyone but Advent who'd get it innately), but really they're not designed to hit small, non-emitting, non-moving targets of that nature. SC should generally not be the anti-mine sweeps of choice (unless you pop for a research upgrade, as I mentioned). (I suggested Advent to have anti-mine fighter inherent because they generally prefer to go heavier on fighters rather than Defense craft, and that fits their philosophy much more tightly.)
I've suggested adding some sort of mine-clearing enhancement to the Cielo cruiser for the TEC. Through upgrades it would allow engagement and quicker destruction of mines over a wider than normal radius when paired with scouts for spotting. The Vasari and Advent would need other solutions, though I like your idea of using strikecraft for the Advent.
Make the deployment of a mine done as a field on purchase, give them some "maintainance" necessity, and minimize the micromanagement necessary to make them an issue and I think they'll be much more useful. Oh yes, and said fields should be spherical around a point, not disc-like flat. Possibly you could add a different deployment orientation as an interface option, such as a plane oriented flat-face toward wherever the layer happened to be at deployment, but that adds complexity.
I don't like the idea of maintenance. I think they are fine without it. We just need a cap, which will probably be different for each side, given that they use mines in different ways. The sphere vs. disc issue is a major one. The need to create barriers means that you need to mine the full volume of space along that border, which means that the mine cap would need to be much higher than what many are calling for. Otherwise the enemy will simply go over or under them. I'm not sure how to solve that without the creation of easy methods of drawing a border around the area you want to have mined, and then having the pattern automatically created to fill the entire volume of space within those boundaries. That calls for a lot of mines though.