Drat. The only other thing I can think of is a signal booster that's tuned to the frequency(ies) that you need. This is the kind of kit used to steal cars, by amplyfing up the feeble signal sent out by keyless-entry cars when you press the door button to unlock. Signal gets picked up by thief's radio-gadget beside the car, boosted hugely, picked up (erroneously!) by fob that's 50 yards away or more, responds with a feeble signal thinking the car's 3 feet away, that in turn is picked up by accomplice with similar radio-gadget standing outside your house, boosted up hugely as it's so feeble, then this boosted signal is strong enough to get back to the car which then unlocks your car. Starting it is the same process, and once a car's started, the engine won't stop even if no key is detected (while they drive away), as that would be a safety hazard!
Maybe you can hunt for a signal booster, but don't blame me if the cops come checking later! 😆