Blake,
It's very hard for me to help if I can't see your code or your data. The problem could be caused by so many things:
- data issue - what is the format of your data? Is it tpk or tiled service. How was it generated?
- an issue in your code
- a bug in our software
You do really need to see if the bug happens on a supported version of our API - 100.5 is what I'd recommend. Have you tried with this version yet?
Appreciate you might not want to share things on a public forum. If you or your customer has a support contract with ESRI you could contact them with a reproducer and data which shows the issue. Again I'd recommend submitting the issue with 100.5 as this release is where our development efforts are concentrated. 10.2.8 is in mature support and quite an old product.
What a lot of people do in your position is to share a very focused application which ONLY shows the data failing to render and they supply a "sanitised" set of data.
I'm not aware of any methods of manually drawing map tiles; they should render without intervention and I'm sure you appreciate this is something we do quite a lot of.
I need more info to help with this; the problem could be so many different things.
Mark