If your hands are too close to your body, you picked the wrong size frame.
By that, I mean that you don't have to have a drop bar, or even a bike designed for a drop bar. People have an absurd fettish with putting a drop bar on every bike and an absurd notion that it will make them faster. Unless you're hell bent on winning and can maintain 20mph+ on a dirt road, aerodynamics don't mean much. If you just want to have fun spinning miles on mixed surfaces, a hardtail with a flat bar or even a rigid mtb would be just fine.
Any bike designed with a drop bar in mind will have a shorter reach and shorter top tube than a flat-bar bike. The reach to the hoods on such a bike should be about the same as the reach to the grips on a flat handlebar. Putting a drop bar on a bike that was designed to fit you with a flat bar will most likely result in a bike that is way too stretched out to be comfortable because the additional reach of the bar + hoods is subtracted from the frame.
For example, my mountain bike (flat bar) has an ETT of around 615mm, and my CX bike has an ETT of 545mm. The respective reaches are 412mm and 377mm. My feet, butt, and hands are in about the same orientation on both bikes when I out my hands on the hoods because the CX bike has a shorter top tube, longer stem, and all that drop bar reach to even it out. If I put a flat bar on the CX, it would feel two sizes too short and a drop bar on the mtb would feel gigantic to me unless I also install the stem backwards.
A bike with a flat bar plus comfy bar ends or some kind of "alt bar" also works well for long miles on dirt.