If you want to disregard the mental health institutes facts all together, Lets use some simple probability instead.

Lets say that the general increase in suicide risk factors is only 51% Because 51%>49% meaning it fits the term "more often than not".
We have some (not all) of the risk factors associated; Hopelessness, Loss of Family, Family Difficulties, Isolation and Being Male (3/4 suicide are males and has been proven to be a risk factor). We also have the loss of our major family protective factor.

In order for the event to have NO suicide increase at all, all 6 factors will need to fall on 49%.

The chance of all factors NOT causing an increase is (49/100)^6 = 1.384...% and that's with swaying the occurrence heavily in your favor.

With a more reasonable split of 65/35 we get (35/100)^6 = 0.183...%. So probability wise, you're outcome isn't looking so strong.

Lets boost your odds even more. Lets say ALL the risk factors associated either cause an increase or not. And the major protective factor lost also either causes an increase or doesn't.

This leaves us with (49/100)^2 = 24.01%. So with our heavily biased outcomes of your claims. It still only 24% probability. 12.2% if we use a more realistic numbers. If including severity of each factor also, that probability drops significantly more.