From the perspective of an outsider who has been following this saga from not-too-afar, drawing liberally from comments made in the many threads on this topic.
Some supporters of the parcel tax believe that they can reach the 2/3 goal on a third try, since the percentage of YES votes rose between the first and second attempts. There are several ways to accomplish this:
1. Increase YES votes while NO votes remain constant - roughly speaking, get out the YES vote;
2. Decrease NO votes while YES votes remain constant - see that some NO voters don't vote;
3. Increase YES votes relative to NO votes with participation increasing or decreasing - count on getting the better end of any change in participation;
4. Flip some NO votes to YES votes.
I don't think you need to pay consultants to decide that the fourth option is the best choice. You don't need to focus on increasing participation, and if you position the election away from other contentious issues, which may drive participation beyond your control, you can focus on persuasion. Mathematically, you gain the most from persuading NO voters to vote YES - each such flip has the net effect of combining both items (1) and (2) from the above list.
I have seen comments from people who say they would have voted YES if X, Y, or Z had happened. Focus on those concerns and you should have a winning margin.
It would be great for someone to put together a presentation on the district's finances. Explain how the district has been funded in the recent past, and why revenues are down. Include the most current numbers that are publicly available. Lots of charts and graphs.
Then, break down the budget into categories, again with charts and graphs. Show data for the recent past. Include forecasts for the near future.
After the pure statement of budgetary facts, present ways to close the budget gap. Include things that you may find unreasonable, if they close the gap - you can filter them out later when you suggest a preferred method (which will presumably be a parcel tax combined with other measures which may already have been adopted).
Try to assign some measurable value to the effects of each choice on closing the gap.
Include numbers, where appropriate, on similar data from surrounding communities.
Finally, make a first cut of the information available for public comment on the web. People may want to challenge your raw data, suggest things you forgot, or otherwise improve the debate.
If you make the process transparent (through public scrutiny), and address the concerns of a small minority who seem ready to accept a parcel tax under some circumstances, I think you can succeed. Your cause is suffering from a lack of trust in the district's management, the presentation of the case for the tax ("support the children and schools!" as if that is a sufficient, standalone case for higher taxes), and pushback against government labor unions.
What I fear is that the proponents of a parcel tax will simply try again without any attempt to address what seems to be the biggest concern among NO voters (automatic raises baked into the union contracts in the current economic environment), with a bigger rah-rah carnival show intended to drown those voters out. More spending on trying to get the tax passed, more spending opposing it, and ugliness all around.
I think the sections of the presentation dealing with how schools are funded, and why things have changed, would make fascinating reading.