ZFW D-side controller described a late hand off and LOA compliance failure event during a sector splitting attempt; reporter suggested improved timing of the position splitting efforts.

Narrative

By LOA; ELD descends the LIT arrival to FL240; initiates a hand off to ZFW30 (MLU-L). ZFW30 enters FL190 or the next lowest available altitude into the data block; initiates a hand off to ZME-Greenwood low. After Greenwood low accepts the hand off; ELD sector descends the aircraft to the altitude displayed in the data block and switches communication to Greenwood low. If the aircraft is not below FL240 before crossing the ZFW/ZME boundary; a point out is required to ZME-PBF-H. ACR X; A LIT arrival wasn't descended or pointed out to PBF-H until on the ZFW/ZME boundary. After pointing ACR X to PBF-H; I descended the aircraft to FL240; handed it off and switched it to Greenwood low; thereby not following the LOA. At the time; the controller who had been the Radar Associate was trying to split off RSN; Sector 90 R and D were overriding me several times with coordination for an aircraft climbing into their sector and clipping sector 71. At the same time; there was an aircraft going to ZHU that needed to be descended for conflict resolution. It was not a good time to try to split the sectors. There were at least 3 times in 2 minutes that there were at least 3 overrides. More than once; it was the R and D from sector 90 and RSN (92). There were also calls from ZHU for hand offs to RSN during this time. Recommendation; either the R or the D call for coordination and decide what you want prior to making the call. Just the coordination over one aircraft took the better part of 3 minutes when all that was needed was to show me the traffic and request me to separate them. Split sectors when the traffic is entering the sector or before. Trying to split a sector when the aircraft are either in the sector or leaving the sector creates extra work.