Gibson model closest to Martin D-28

troubador , I can totally understand the budget restrictions thing, or even just the unwillingness to drop a dump truck load of money for a particular guitar. 

So, you're options here could be plenty.  I mean, with acoustics, there's always that "piece of wood" luck of the draw factor in there.  I'd suggest going and playing (trying out) as many guitars as you can get your hands on and I'm pretty sure you'll eventually find something that has a sound close to what you're looking for that you'll really like.

Don't restrict yourself to one brand though, allow yourself to explore all the options.   I've never tried Eastman myself, but as @sleigh , and many others have said, they make fantastic guitars.  I personally love Alvarez and the way they make their guitars reminds me of Martin actually (and some other models like Taylor, so both worlds covered).

But you could even come across a Yamaha, or Takamine, or Seagull, or whatever that blows your socks off.  You could even try some of the entry level Martins.  They of course have that Martin sound and you might just be amazed at how good many of Martin's "cheap" guitars sound.  I had one once that I absolutely loved and would still have to this day had I not had to sell it at the time (you know how it goes, sometimes times are tough).

So just go look around and have some fun playing tons of guitars.  It may start wide at first, but it will narrow down.  The secret is not trying to find what you want, it's becoming sure of what you don't want, and then what's left will be what you pick from.

Good luck in your search!  Have fun with it! 

or you might look at the AMI Sigma martin designed models. I love my 000m-15 and I played it against the Martin version with my dealer and neither of us could tell which was which.

 Like @sleigh , I'm a huge Eastman fan, but I think their voice is different than either Martin or Gibson... a little more clarity, balance, and high end sparkle than the typical Martin sound (I actually prefer the Eastman voice).