Jim, I did have some success connecting the ST60 Multi's NMEA+ to RS232 RXD and NMEA- to RS232 GND, *AS LONG AS* the computer was ungrounded. See Actisense's comments regarding not grounding the NMEA- in most cases. With the laptop on batteries or even its AC adapter, it worked fine. However when I plugged the laptop into another device on ship's DC, no more NMEA from the Multi.
Perhaps the IOGear is floating wrt ground (we wish) or you could try the Digital Yacht usb-serial-NMEA reviewed on Panbo:
Panbo: The Marine Electronics Weblog: DY NMEA 0183 to USB, looks handy
List price is about double the IOGear but you'd avoid another adapter.
For a time I used a Noland N183-41 NMEA multiplexer, (discontinued version, borrowed from a friend) which took NMEA in and provided a floating NMEA output as well as RS232. You might find something like that on eBay.
Eventually, I broke down and got the Raymarine E85001... it has the advantage of providing many more sentences, as well as NMEA and RS232 out.
edit: Come to think of it (and re-reading your question), a simple circuit for that application could be simply an Opto-isolator, with a 1K resistor in series with the input/NMEA side (the Multi itself uses 4 2.2k in parallel in series with a PC357 opto) then the opto collector to +12 (with another 1k or so in series for good measure) and the opto emitter to RS232 in. You might need a 10k pulldown or so on RS232, but usually switching from open circuit to +12 would work even without a negative source.
I hope this verbal schematic makes sense, if so it's only about $5-10.
I'm off to bilgeclean and bottompaint but would be delighted to prototype the circuit, test and tweak the resistor values in exchange for help with 46' of wax job. ;-)