I've managed to solve this, without using the mentioned GRASS tools or topological functions.
Basically I take all start- and endnodes, put them in a new, temporary table, put a buffer around them, union the buffer objects, and move all found nodes in each buffer to the centroid of the buffer.
When that's done I move the original begin and end points to the new location.
Easier than expected, and still fast, but I expected PostGIS to have some built-in function for this - that would be even quicker.
Edit: in the interest of giving back to the community, this is my (quite crappy) code for now.
drop table if exists nodes;
drop table if exists nodes2;
drop table if exists buffers;
-- Get Start and End nodes
select ST_StartPoint(wkb_geometry) startnode, ST_EndPoint(wkb_geometry) endnode, ogc_fid into nodes from sourceTable;
-- Combine all nodes into one table for easier queries
select startnode node, ogc_fid into nodes2 from nodes;
insert into nodes2 select endnode node, ogc_fid from nodes;
-- Some indexes to speed everything up
CREATE INDEX nodesstart_idx ON nodes USING gist (startnode);
CREATE INDEX nodesend_idx ON nodes USING gist (endnode);
CREATE INDEX nodes2_idx ON nodes2 USING gist (node);
CREATE INDEX nodes_ogcfid_idx ON nodes USING btree (ogc_fid ASC NULLS LAST);
-- Create buffers, combine them, split combined objects again
select (ST_Dump(ST_Union(ST_Buffer(node, 1)))).geom geom into buffers from nodes2;
CREATE INDEX buffers_idx ON buffers USING gist (geom);
-- Update start/end nodes table
UPDATE nodes SET startnode = ST_Centroid((select geom from buffers WHERE geom && startnode));
UPDATE nodes SET endnode = ST_Centroid((select geom from buffers WHERE geom && endnode));
-- Update original points
update sourceTable set wkb_geometry = ST_SetPoint(
ST_SetPoint(wkb_geometry, 0, (select startnode from nodes where ogc_fid=sourceTable.ogc_fid)),
ST_NumPoints(wkb_geometry) - 1, (select endnode from nodes where ogc_fid=sourceTable.ogc_fid));
DROP TABLE nodes;
DROP TABLE nodes2;
DROP TABLE buffers;