The off network PTT simplex mode is Direct Talk, not to be confused with Direct Connect which used the NEXTEL iDEN network. NEXTEL is long gone but these phones can be used in Direct Talk (DT) mode. One gotcha with them is they must have a SIM card that was previously activated on NEXTEL or another iDEN network in order to enter DT mode. This is required because the DT protocol uses 1 plus the area code and phone number that was assigned to the phone to form the 11 digit Private ID used by the DT system. These phones will not enter DT mode without a SIM card that was previously activated on a NEXTEL or other iDEN network.
The DT feature is known generically as MOTOTALK.
en.wikipedia.org
The DTR410/550/650 radios, DLR1020/1060 radios, and the new DTR600/700 radios are the modern day implementation of the old MOTOTALK platform. The DTRs and DLRs were coded differently (supposedly on purpose) to be incompatible with the DT feature in NEXTEL phones but they use the same digital FHSS system. The DTRs and DLRs were spinoffs from the the off network DT feature in NEXTEL phones. I suspect the DTRs and DLRs became incompatible with the DT feature in NEXTEL phones when more features were added.
If your bin of old DT-capable NEXTEL phones have SIM cards in them, then you probably can get them working with each other in DT mode. My wife (g/f at the time) and I have owned i355 NEXTEL phones and we used them in DT mode and they worked great. The i355 is a good one to use. Factory fresh new batteries are still available for the i355 because the legacy DTR410/550/650 models use the same hi-capacity battery. I own a small fleet of DTR650 radios and I re-batteried them with factory fresh new batteries a couple of years ago so I know you can still get new batteries for them.