Tombstones are usually the result of confluence of multiple factors. Pad design, print location, print consistency, part placement and profile, to name but a few.

Check the pad sizes and ensure they are not too big, check the paste deposits for location and consistency volume differences can contribute to the problem. Also check the part placement poor alignment is a contributing factor. Look to see if the board design is one end of the part attached to a heat sink that could cause differential heating in the reflow oven.

Profile often is often difficult to change and is usually a marginal effect but a slow transition through the melt point is desirable. Finally there are anti-tombstone alloys with "phased reflow" which open the process window and can have a dramatic effect on the incidence of tombstones.

Tomb stoning is a problem when going to lead free. Reflow profiles and component finishes will have the biggest impact on this. A profile with a high temperature soak may solve the issue I would recommend a soak at 200C prior to ramping to spike. There are some solder pastes available with different powder distributions and alloy types that will also offer an improvement. One alloy that is known to eliminate tomb stoning is Sn100C.

I would first try to profile them out using the high soak. Additionally try to identify if a specific component manufacturer has a high rate than another.

There are several factors that impact the frequency of component tombstoning.

Factors that impact tombstoning include:
Printed circuit board component pad design
Solder paste printing accuracy
Solder paste volume consistency from one of the component's pads to the other,
Component placement accuracy
Reflow profile precision, etc.

Using lead free components with tin lead solder paste certainly is not an ideal situation. You now have the component lead finish material, most likely 100% tin, and the tin lead solder paste reflowing at different temperatures.

My suggestion is to evaluate all the factors that influence tombstoning to insure they are well understood and optimized.

If you already have lead free components, unless there is a compelling reason not to do so, I would move to the conversion to lead free solder paste as soon as possible. We (Speedline Technologies) has a presentation titled "Component Tombstoning and Mid Chip Solder Balls Causes and Prevention" that I will be happy to send you if you contact me.