Darvin, I think your main problem is that you've resigned yourself to being a "slow Demigod"
It's not that I've consigned myself to having a slower demigod, but rather that my issue is when I'm playing a slower demigod. Getting speed items helps only so much, because enemy demigods can do the same to you.
As I said, the primary issue is that when the enemy is faster than you, even by a slight margin (or if they have skills like maim or diseased claws) then they're just kiting you all the way back to your tower line, and usually that's enough to bring you to the brink of death, if not kill you. If you're faster than them, however, there's no problem.
Which DG are you talking about, by the way?
It was actually a game as unclean beast that prompted me to make this post, and Sedna was the faster demigod. I was trying to whittle away her mana with a continual barrage of spits, but as soon as I ventured too far from my towers she just began an all out battle of attrician. I quickly saw that she was going to win in the long run, so chugged a potion to get back to 80% health and started to run, but all that health was whittled away before I got back to my tower line.
The real challenge on this map is beating two tower farming rooks.
I've done that; quite fun but also quite risky. Obviously you can't hold the gold mine flag against competent enemies, but there are some great DG counters. Regulus and TB are great for breaking a Rook's advance with their AoE damge, for instance.
As for the gold mine flag, just keep it locked.
That doesn't seem smart to me. I can certainly see locking it after you take it, but "keeping it locked" seems woefully impractical. In addition to being quite expensive to perpetually keep something locked, you'll easily spend half your time running back and forth between the lane and the flag to keep applying new locks. If you're actually outplaying an enemy well enough that you can afford to make a trip like that every 45 seconds, I don't think you need the locks in the first place.