your connex will cover the following frequencies as is out of the box 28.065 to 28.505, as you learned this is not useful as the radio only has am and
fmmodes of transmitting. on the ten meter amatureband (us) frequenciesof 28.000-28.300 are only allowed to use cw (continuouswave or morsecode). frequencies of 28.300-28.500 are used for single sideband ( upper side band will be used on 10m).
your radio does not have ssb (single side band) mode of operation so its cannot be used. the frequencies the entry level or technician ham licence will cover. you will need to upgrade your licence to a general or extra class to take advantage of your radio on 10m (general or extra class operators can use between 28.000-29.700). am mode is common between 29.000-29.200 where fm mode is common around 29.510-29.700. simplex operation is generally only used on 29.600. (simplex is direct transmission and receiving on a common frequency, duplex would be repeater use where input and output frequencies are split. something your connex cannot do. a rci 2950dx with a tone board would be able to however.
if you modify it for expanded or export frequency it will cover from 25.615 -28.305. covering the cb band. you now see why these are not 10m radios in the us and why they can be classified as illegal. they cannot operate legally regardless of the operators intentions. (at least in the us)