It ain't gonna work the way you want it to.

The only way I can see it working reasonably is for 2 awards

NYC-TLV-NYC then NYC MNL-NYC (or vice versa)

A OW award ticket is the same cost in miles as a RT.

TLV is considered a part of Europe with respect to Skyteam.

As for NYC-TLV-MNL-NYC

This would be a N. America-Europe-Asia-N. America (no layover is alowed in this one without a RTW ticket) routing which would be either 1 RTW award or 3 trans-oceanic OW awards (which is the same cost in miles as 3 transoceanic RT awards) I know that Europe to Asia is not really trans-oceanic, but it is treated that way as far as the awards are concerned.

To summerize how I see your options:

1. One RTW award NYC-TLV-MNL-NYC

2. Two intercontinental RT awards NYC-TLV-NYC and NYC-MNL-NYC.

or

3. Three OW intercontinental awards (that cost the same as three RT intercontinental awards) NYC-TLV-MNL-NYC.

Choose your poison.