I like Suburban Jungle Lifes' advice because it agrees with what I am doing. 
Unless you have the money time and energy on tap for a complete reno , which as noted may not solve all the problems, my recommendation would be to go after these problems one at a time.
I am in my second summer in a house with a lawn that would be too expensive to renovate and irrigate so I am going after a multitude of problems. This is our fourth and hopefully last house and I have done tier one lawns previously. I never liked the idea of glyphosating a lawn. (This is a personal preference probably arising from a lack of confidence in St. Louis weather)
I worry about ending up with the Bonneville Mud Flat. For whatever reason, big white patches from Tenacity don't bother me at all. The difference in the bleaching/whitening is pretty interesting and highlights different species existing in the hodge podge that is my lawn.
It takes a couple or three years to beat a lawn into Tier one or two submission.
One thing I "think" I may be noticing is that since I have been spraying lawn chemicals all over the place I have the impression that the moles like my lawn less. I could be imagining this. I haven't even sprayed grub spray yet but I do have a jug of imicloprid on hand and it will be included in most future sprays.
It probably is possible to fix many of your problems in conjunction with a major reno. Depends on the budget. I don't have experience with getting rid of creeping bentgrass. But I think there are grassy weed herbicides that will do the job for you.
The specific for mossy weeds is Carfentrazone (Quicksilver)
Unless you have the money time and energy on tap for a complete reno , which as noted may not solve all the problems, my recommendation would be to go after these problems one at a time.
I am in my second summer in a house with a lawn that would be too expensive to renovate and irrigate so I am going after a multitude of problems. This is our fourth and hopefully last house and I have done tier one lawns previously. I never liked the idea of glyphosating a lawn. (This is a personal preference probably arising from a lack of confidence in St. Louis weather)
I worry about ending up with the Bonneville Mud Flat. For whatever reason, big white patches from Tenacity don't bother me at all. The difference in the bleaching/whitening is pretty interesting and highlights different species existing in the hodge podge that is my lawn.
It takes a couple or three years to beat a lawn into Tier one or two submission.
One thing I "think" I may be noticing is that since I have been spraying lawn chemicals all over the place I have the impression that the moles like my lawn less. I could be imagining this. I haven't even sprayed grub spray yet but I do have a jug of imicloprid on hand and it will be included in most future sprays.
It probably is possible to fix many of your problems in conjunction with a major reno. Depends on the budget. I don't have experience with getting rid of creeping bentgrass. But I think there are grassy weed herbicides that will do the job for you.
The specific for mossy weeds is Carfentrazone (Quicksilver)