Nice old drill press but I'd have the same reservations about moving it too without a forklift (I don't have one). Wouldn't try moving it from original location vertical, it would have to be horizontal if moving farther than a city block. Laying it down seems like it would have to be a controlled tip-over, a roll-back wrecker would be safer/easier/cheaper considering what you currently don't have for rigging equipment. I moved my entire machine shop by myself (lathe, Bridgeport, surface grinder, 800 lb. granite plate, etc.) but hired a roll-back to move the 5,000 lb. jig borer, It was $200 (IIRC) to transport it 40 miles and he placed it upright (carefully) on the concrete apron of my garage. Money well spent to avoid disaster/damage/injury. For all the other machinery I built a gantry made from wood on surplus heavy duty casters and used a chain fall at the top header. It worked just fine lifting the 2,000 lb. Bridgeport and all else.
Since that DP is likely top heavy I'd lift it with the gantry enough to slide some machine skates under it (which can be shop made) and then roll it all to final location. Top secured against tipping by chain-fall, weight supported by skates rolls easier so the gantry is along for the ride and doesn't allow swinging the DP when traveling. Between machine skates, a toe jack, and the gantry I can move any/all of the machinery and do that periodically when I need more space for projects. Can provide details, CAD drawings, and/or personal experience if requested. You'll have to spend a few bucks to do this but you already knew that. Additional devices for moving heavy machinery will be used later so it's not wasted money. Gantry plus chain fall was under $250. Wood/hardware for gantry can be dis-assembled for other uses or stored.
If you were closer I'd drive over to help but I'm up to the elbows with HVAC + ducting replacement for another month or two.