To me, this seems to be pretty clear and I almost feel embarassed questioning it...just follow the chain logically.
1) You can use the Inpiring/Healing Word POWER (for emphasis) once per day. We have just established that unlike the base class, the multi-class can only use this POWER once per day. This clearly indicates the rules regarding the ACTIVATION of this power has changed.
2) Once you activate a power, you gain the full effects of that power unless otherwise stated. For example, the Warrior of the Wild mark only lasts until the end of your next turn (in the errata). This is explicitly stated. This both states that you gain an ACTIVATION of the power, but also restricts its EFFECT.
3) The Warlord and Cleric MC Feats do not say anywhere that they change the EFFECT of the powers they grant, only how often the POWER can be used. Also, the Feat does not say you gain the EFFECT of the power once per day, but the USE of the power; this is the same as giving the power through the Feat, just with a restriction to its ACTIVATION.
4) The EFFECT of Healing/Inspiring Word is that, twice per encounter, you can use it to cause the target to spend a healing surge. It does not say that this second surge requires another use of Healing/Inspiring Word...otherwise the full EFFECT of the power would be gained, allowing for two more healing surge expenditures.
5) The rule of 4E is that unless a rule specifically says something contradictory, you should follow the standard rule. In this case, the Feat specifically states that the the normal ACTIVATION of the power is different, but says nothing about the EFFECT of the power once activated.