The post above mine sums it up nicely. I've found searching Craigslist, and checking the tandemclassifieds page to be a good way to get a feel for the used market. $2k used will buy you quite a few bikes made in the last 20 years. $2k new is substantially more restrictive. If the budget is firm then I'd aim closer to $1600, and leave the last $400 for any needed adjustments or repairs. For example, I recently bought a used tandem for $1500. I spent around $180 getting it shipped to me (insured), $77 on two new tires, $15 on 2 new tubes (much different tire size, plus a spare), and $60 for 3 chains. I also swapped in around $50 in parts from my parts shelf.
It looks like you aren't an unusual height. I'm 6' tall if I wear thick enough socks and my primary stoker/wife is 5'4". Our tandem riding is minor compared to most around here, I'd guess around 500 miles/year, but for the type and frequency we ride I've found that close is well close enough to keep us happy and comfortable. If you were say a 5' captain and a 6' stoker it would be much more difficult.
When you say bike trails, I'm assuming you mean paved, but if those are gravel that requires a bit more attention. Many tandems clear wider tires without issue, but not all.
Most tandems I see used are road drop bars in the front, and sometimes the stoker. It looks like your current one may be set up for flat bars. Do you have a preference?
What are your goals for your upgrade? Do you have reliability issues, weight concerns, general "this seems like a cheap bike" concerns, don't like the way the current one handles, etc?