Is it permissible to do an inhaled blow at the narrow end of the shofar to fulfill the obligation of shofar blowing?
I have tried this and it is relatively easy to generate the same sound for an inhaled blow as an exhaled one.
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Based on the following Malbim1 I would venture a GUESS that this is problematic:
"וכן למד משם שיהיה פשוטה לפניה ולאחריה ממה שכתוב לשון "והעברת שופר". שהגם שמצאנו לשון "העברה" על הקול – "ויעבירו קול במחנה", על שהקול עובר ומתפשט בכל מקום, לא יצדק על השופר. והיה לו לומר "והעברת קול שופר". ועל כרחך פירושו שתעבירו את השופר עצמו, שהתוקע תקיעה פשוטה מעביר רוח פיו דרך השופר, לא כן המריע, אין רוח עובר ביושר, כי פורט על פיו בלשונו"
A rough explanation of this malbmim is as follows. There is a verse which states that we need to "pass a shofar, truah" (ותעביר שופר תרועה). The Malbim understands this verse to mean that we need to pass our air or breath through the shofar uninterrupted.
According to the Malbim, this is the source for the uninterrupted sound of a Tikiah that we sound on Rosh HaShana. This contrasts with a truah which is an sound formed by interrupting the air flow through the shofar.
Now, if we can assume that the above understanding of the verse has halachic validity, then we see that the Torah instructs us to pass air through the Shofar, not to draw air out of the shofar.
As such, we could reasonably conclude that a sound formed by drawing air out of the shofar is not a valid means of producing a shofar sound and therefore one cannot fulfill their halachic obligation this way.
This would be so even though we also paskin that "all sounds are kosher in a Shofar". We would have to reinterpret that halacha to mean that all sounds legitimately made in the shofar are kosher.
A sound made by passing air is legitimate -- and therefore it is kosher whether it is loud or soft, high pitched or low, etc. On the other hand, a sound made by drawing air would be illegitimate and would be pasul (nullified) regardless of how it sounds.
Of course, this assumes that we actually paskin according to the Malbim's understanding of the verse. And that assumption may be false. I don't know, which is why I am offering it merely as a suggestion.