^ The way a different bulb would work with the existing flasher is if it pulls a lot more current, because the forward drop (heat) in the old style mechanical flasher is what makes them toggle on and off. If the bulb were designed to draw the extra current unnecessarily (besides combatting this issue) that current would be converted to heat AT the bulb, which is something an incan bulb can tolerate more of while an LED bulb needs to stay cooler for good lifespan.
You can create the extra load for that with your existing bulbs by just putting a ballast resistor in parallel on the wiring to the bulbs, same as people do to get rid of the bulb-out warning messages on vehicles switched to LED and equipped with a bulb-out detection feature, or to just solve hyperflash, get an LED compatible flasher module. They work on a timer IC rather than current toggling on/off state so don't depend on how much load the bulbs are.
The LED compatible flasher module is the best option.
There are bulbs with the built in resistor, some have a fan added, some have a time-out IC to keep them from flashing for long so they don't overheat as badly. I've also seen a few with a separate ballast resistor on the wiring pigtail to them and you mount the resistor on metal to heatsink it... with some thermal compound aka heatsink grease, and ideally, not an exterior painted metal as the heat can damage paint.
You can search for "red turn signal no hyper flash resistor" or something like that, but I have not tested any of them in a 3rd gen. Explorer so can't recommend one specifically. I'd be hesitant to do so anyway because I doubt any will have as long a lifespan as a standard long life, incan bulb. Bulbs that fail before you realize it, so don't work at all are probably worse than dimmer bulbs.