If this was a legitimate life estate that will meet the IRS test for a stepped up basis, then your problem is finding the value as of March 2016.
The only reliably proven value you have is $90,000 in 2017. I think that if you used a value of $150,000 based on the gift letter from September 2014, and you are audited, you will be in trouble. Using that value will create a $60,000 capital loss. You can use that loss to offset other capital gains (such as from sale of stocks). If have no capital gains to offset, you can deduct $3000 of the loss each year and carry the rest forward for up to 20 years. That gives the IRS 23 years to audit your claimed loss.
You have no reliable proof that $150,000 was an accurate value in 2014. It could have been a false value made up by you or your mom for self-serving purposes, or it could have been her unrealistic hope for a value. And even if $150,000 was an accurate value, it is unlikely (unless there was some kind of disaster) that the house held its value until March 2016 and then suddenly lost 40% of its value in the next 15 months. It seems more likely that the house was on a long slow decline, or that it was never worth $150,000 and that was just your mom's wishful thinking.
There will be someone even in rural Hungary who is qualified to give an estimate of local property values. Such as from sales of other similar properties from a similar time frame (Spring 2016). Of course, it may be difficult to contact such a person.
You say you don't want to claim losses. In that case, the least controversial value you could report is that it was worth $90,000 on the day she died. And really, unless something terrible happened to the neighborhood or the Hungarian economy, that's probably correct anyway -- the house was probably worth about the same in March 2016 as it was worth in July 2017. If you have sales expenses like taxes and fees, that will create a small one-time deductible loss which is unlikely to raise concerns.
