Typically open enrollment starts in October for the next calendar year. So you are probably keeping your current plan through 12/31, then starting your new plan on 1/1/17. You may still have time to schedule it this year while your better insurance is available. Every year corporate health insurance benefits transfer more cost from employer to employee - it's been heading this way for a long time, and private payors are happy to respond to corporate demands to facilitate this. Your employer does have better plans available, they choose not to buy them.
Generally speaking, you're better off taking the HDHP and fully funding your HSA every year. Then you can use the HSA funds to pay your deductible, Rx, and copays at the doctor. You pay 100% of cost until the deductible is met, then share costs with insurance (copays, sometimes a percentage of costs via coinsurance) until you hit the out of pocket maximum. So a typical plan may have a $2000 deductible, $4000 oop max, 20% coinsurance. You'll pay 100% of the bills up to 2k, then 20% of the bills from 2-4k, then anything above that is free to you.