Another update...
Yesterday I switched to using the MQTTClientGateway from tomkxy's branch. It is acting as a MQTT client instead of as a broker, as I think it should. I mean, if you have installed Openhab and thinking of using MQTT instead of serial as communication I think installing a Mosquitto broker (for example) probably is not a big deal.
There are obvious benefits to using a "real" broker in that you can have several clients subscribing to the messages at once. This also lets you monitor the messages sent through the broker.
It works great and I now get all the values to Openhab without problems. It even runs on my UNO with the Ethernet shield, even though several persons have said the memory would not be sufficient. Thanks tomkxy!
/Johan